TSTP Solution File: LAT274-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT274-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:32:36 EDT 2022
% Result : Unsatisfiable 2.41s 1.80s
% Output : Proof 2.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : LAT274-2 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 13:06:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 2.41/1.80 % SZS status Unsatisfiable
% 2.41/1.80 % SZS output start Proof
% 2.41/1.80 tff(c_in_type, type, (
% 2.41/1.80 c_in: ( $i * $i * $i ) > $o)).
% 2.41/1.80 tff(tc_prod_type, type, (
% 2.41/1.80 tc_prod: ( $i * $i ) > $i)).
% 2.41/1.80 tff(t_a_type, type, (
% 2.41/1.80 t_a: $i)).
% 2.41/1.80 tff(v_r_type, type, (
% 2.41/1.80 v_r: $i)).
% 2.41/1.80 tff(c_Pair_type, type, (
% 2.41/1.80 c_Pair: ( $i * $i * $i * $i ) > $i)).
% 2.41/1.80 tff(v_sko__4mj_type, type, (
% 2.41/1.80 v_sko__4mj: ( $i * $i * $i ) > $i)).
% 2.41/1.80 tff(v_a_type, type, (
% 2.41/1.80 v_a: $i)).
% 2.41/1.80 tff(v_S_type, type, (
% 2.41/1.80 v_S: $i)).
% 2.41/1.80 tff(v_L_type, type, (
% 2.41/1.80 v_L: $i)).
% 2.41/1.80 tff(v_b_type, type, (
% 2.41/1.80 v_b: $i)).
% 2.41/1.80 tff(v_sko__4mi_type, type, (
% 2.41/1.80 v_sko__4mi: ( $i * $i * $i ) > $i)).
% 2.41/1.80 tff(c_Tarski_OisLub_type, type, (
% 2.41/1.80 c_Tarski_OisLub: ( $i * $i * $i * $i ) > $o)).
% 2.41/1.80 tff(v_cl_type, type, (
% 2.41/1.80 v_cl: $i)).
% 2.41/1.80 tff(v_A_type, type, (
% 2.41/1.80 v_A: $i)).
% 2.41/1.80 tff(c_lessequals_type, type, (
% 2.41/1.80 c_lessequals: ( $i * $i * $i ) > $o)).
% 2.41/1.80 tff(tc_set_type, type, (
% 2.41/1.80 tc_set: $i > $i)).
% 2.41/1.80 tff(c_Tarski_Ointerval_type, type, (
% 2.41/1.80 c_Tarski_Ointerval: ( $i * $i * $i * $i ) > $i)).
% 2.41/1.80 tff(v_sko__4mk_type, type, (
% 2.41/1.80 v_sko__4mk: ( $i * $i * $i ) > $i)).
% 2.41/1.80 tff(c_emptyset_type, type, (
% 2.41/1.80 c_emptyset: $i)).
% 2.41/1.80 tff(1,assumption,(~c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a))), introduced(assumption)).
% 2.41/1.80 tff(2,plain,
% 2.41/1.80 (c_Tarski_OisLub(v_S, v_cl, v_L, t_a) <=> c_Tarski_OisLub(v_S, v_cl, v_L, t_a)),
% 2.41/1.80 inference(rewrite,[status(thm)],[])).
% 2.41/1.80 tff(3,axiom,(c_Tarski_OisLub(v_S, v_cl, v_L, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_4')).
% 2.41/1.80 tff(4,plain,
% 2.41/1.80 (c_Tarski_OisLub(v_S, v_cl, v_L, t_a)),
% 2.41/1.80 inference(modus_ponens,[status(thm)],[3, 2])).
% 2.41/1.80 tff(5,plain,
% 2.41/1.80 (c_in(v_b, v_A, t_a) <=> c_in(v_b, v_A, t_a)),
% 2.41/1.80 inference(rewrite,[status(thm)],[])).
% 2.41/1.80 tff(6,axiom,(c_in(v_b, v_A, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 2.41/1.80 tff(7,plain,
% 2.41/1.80 (c_in(v_b, v_A, t_a)),
% 2.41/1.80 inference(modus_ponens,[status(thm)],[6, 5])).
% 2.41/1.80 tff(8,plain,
% 2.41/1.80 (^[V_z: $i, V_S: $i, V_L: $i] : refl((c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) <=> (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))))),
% 2.41/1.80 inference(bind,[status(th)],[])).
% 2.41/1.80 tff(9,plain,
% 2.41/1.80 (![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) <=> ![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.41/1.80 inference(quant_intro,[status(thm)],[8])).
% 2.41/1.80 tff(10,plain,
% 2.41/1.80 (![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) <=> ![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.41/1.80 inference(rewrite,[status(thm)],[])).
% 2.41/1.80 tff(11,plain,
% 2.41/1.80 (^[V_z: $i, V_S: $i, V_L: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) <=> ((~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))), ((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (((~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))), rewrite((((~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))), ((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))))), (((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a)) <=> ((c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) | c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a)))), rewrite(((c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) | c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a)) <=> (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))), (((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a)) <=> (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))))),
% 2.41/1.80 inference(bind,[status(th)],[])).
% 2.41/1.80 tff(12,plain,
% 2.41/1.80 (![V_z: $i, V_S: $i, V_L: $i] : ((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a)) <=> ![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.41/1.80 inference(quant_intro,[status(thm)],[11])).
% 2.41/1.80 tff(13,axiom,(![V_z: $i, V_S: $i, V_L: $i] : ((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0')).
% 2.41/1.80 tff(14,plain,
% 2.41/1.80 (![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.41/1.80 inference(modus_ponens,[status(thm)],[13, 12])).
% 2.41/1.80 tff(15,plain,
% 2.41/1.80 (![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.41/1.80 inference(modus_ponens,[status(thm)],[14, 10])).
% 2.41/1.80 tff(16,plain,(
% 2.41/1.80 ![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.41/1.80 inference(skolemize,[status(sab)],[15])).
% 2.41/1.80 tff(17,plain,
% 2.41/1.80 (![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.41/1.80 inference(modus_ponens,[status(thm)],[16, 9])).
% 2.41/1.80 tff(18,plain,
% 2.41/1.80 (((~![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | (c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))) <=> ((~![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))),
% 2.41/1.80 inference(rewrite,[status(thm)],[])).
% 2.45/1.80 tff(19,plain,
% 2.45/1.80 ((c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a) | c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a))) <=> (c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))),
% 2.45/1.80 inference(rewrite,[status(thm)],[])).
% 2.45/1.80 tff(20,plain,
% 2.45/1.80 (((~![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | (c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a) | c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))) <=> ((~![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | (c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a))))),
% 2.45/1.80 inference(monotonicity,[status(thm)],[19])).
% 2.45/1.80 tff(21,plain,
% 2.45/1.80 (((~![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | (c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a) | c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))) <=> ((~![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))),
% 2.45/1.80 inference(transitivity,[status(thm)],[20, 18])).
% 2.45/1.80 tff(22,plain,
% 2.45/1.80 ((~![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | (c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a) | c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))),
% 2.45/1.80 inference(quant_inst,[status(thm)],[])).
% 2.45/1.80 tff(23,plain,
% 2.45/1.80 ((~![V_z: $i, V_S: $i, V_L: $i] : (c_in(v_sko__4mi(V_S, v_r, V_z), V_S, t_a) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a))),
% 2.45/1.80 inference(modus_ponens,[status(thm)],[22, 21])).
% 2.45/1.80 tff(24,plain,
% 2.45/1.80 (c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a)),
% 2.45/1.80 inference(unit_resolution,[status(thm)],[23, 17, 7, 4])).
% 2.45/1.80 tff(25,plain,
% 2.45/1.80 (c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a)),
% 2.45/1.80 inference(unit_resolution,[status(thm)],[24, 1])).
% 2.45/1.80 tff(26,plain,
% 2.45/1.80 (c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)) <=> c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))),
% 2.45/1.80 inference(rewrite,[status(thm)],[])).
% 2.45/1.80 tff(27,axiom,(c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 2.45/1.80 tff(28,plain,
% 2.45/1.80 (c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))),
% 2.45/1.80 inference(modus_ponens,[status(thm)],[27, 26])).
% 2.45/1.80 tff(29,plain,
% 2.45/1.80 (^[V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : refl(((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))) <=> ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))),
% 2.45/1.80 inference(bind,[status(th)],[])).
% 2.45/1.80 tff(30,plain,
% 2.45/1.80 (![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))) <=> ![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))),
% 2.45/1.80 inference(quant_intro,[status(thm)],[29])).
% 2.45/1.80 tff(31,plain,
% 2.45/1.80 (![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))) <=> ![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))),
% 2.45/1.80 inference(rewrite,[status(thm)],[])).
% 2.45/1.80 tff(32,plain,
% 2.45/1.80 (^[V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : rewrite((((~c_in(V_x, V_S, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a)))) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))) <=> ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))),
% 2.45/1.80 inference(bind,[status(th)],[])).
% 2.45/1.80 tff(33,plain,
% 2.45/1.80 (![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (((~c_in(V_x, V_S, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a)))) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))) <=> ![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))),
% 2.45/1.80 inference(quant_intro,[status(thm)],[32])).
% 2.45/1.80 tff(34,axiom,(![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (((~c_in(V_x, V_S, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a)))) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0')).
% 2.45/1.80 tff(35,plain,
% 2.45/1.80 (![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))),
% 2.45/1.80 inference(modus_ponens,[status(thm)],[34, 33])).
% 2.45/1.80 tff(36,plain,
% 2.45/1.80 (![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))),
% 2.45/1.80 inference(modus_ponens,[status(thm)],[35, 31])).
% 2.45/1.80 tff(37,plain,(
% 2.45/1.80 ![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))),
% 2.45/1.80 inference(skolemize,[status(sab)],[36])).
% 2.45/1.80 tff(38,plain,
% 2.45/1.80 (![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))),
% 2.45/1.80 inference(modus_ponens,[status(thm)],[37, 30])).
% 2.45/1.80 tff(39,plain,
% 2.45/1.80 (((~![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))) | ((~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a)) | c_in(c_Pair(v_sko__4mi(v_S, v_r, v_b), v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ((~![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a)) | c_in(c_Pair(v_sko__4mi(v_S, v_r, v_b), v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 2.45/1.81 inference(rewrite,[status(thm)],[])).
% 2.45/1.81 tff(40,plain,
% 2.45/1.81 ((~![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))) | ((~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a)) | c_in(c_Pair(v_sko__4mi(v_S, v_r, v_b), v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 2.45/1.81 inference(quant_inst,[status(thm)],[])).
% 2.45/1.81 tff(41,plain,
% 2.45/1.81 ((~![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : ((~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)) | c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a)) | c_in(c_Pair(v_sko__4mi(v_S, v_r, v_b), v_b, t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[40, 39])).
% 2.45/1.81 tff(42,plain,
% 2.45/1.81 ((~c_in(v_sko__4mi(v_S, v_r, v_b), v_S, t_a)) | c_in(c_Pair(v_sko__4mi(v_S, v_r, v_b), v_b, t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 2.45/1.81 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 2.45/1.81 tff(43,plain,
% 2.45/1.81 (c_in(c_Pair(v_sko__4mi(v_S, v_r, v_b), v_b, t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 2.45/1.81 inference(unit_resolution,[status(thm)],[42, 25])).
% 2.45/1.81 tff(44,plain,
% 2.45/1.81 (^[V_z: $i, V_S: $i, V_L: $i] : refl((c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))))),
% 2.45/1.81 inference(bind,[status(th)],[])).
% 2.45/1.81 tff(45,plain,
% 2.45/1.81 (![V_z: $i, V_S: $i, V_L: $i] : (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ![V_z: $i, V_S: $i, V_L: $i] : (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.45/1.81 inference(quant_intro,[status(thm)],[44])).
% 2.45/1.81 tff(46,plain,
% 2.45/1.81 (![V_z: $i, V_S: $i, V_L: $i] : (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ![V_z: $i, V_S: $i, V_L: $i] : (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.45/1.81 inference(rewrite,[status(thm)],[])).
% 2.45/1.81 tff(47,plain,
% 2.45/1.81 (^[V_z: $i, V_S: $i, V_L: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) <=> ((~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))), ((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> (((~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))))), rewrite((((~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ((~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))), ((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ((~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))))), (((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (((~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))), rewrite((((~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))), (((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))))),
% 2.45/1.81 inference(bind,[status(th)],[])).
% 2.45/1.81 tff(48,plain,
% 2.45/1.81 (![V_z: $i, V_S: $i, V_L: $i] : ((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> ![V_z: $i, V_S: $i, V_L: $i] : (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.45/1.81 inference(quant_intro,[status(thm)],[47])).
% 2.45/1.81 tff(49,axiom,(![V_z: $i, V_S: $i, V_L: $i] : ((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_z, v_A, t_a))) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1')).
% 2.45/1.81 tff(50,plain,
% 2.45/1.81 (![V_z: $i, V_S: $i, V_L: $i] : (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[49, 48])).
% 2.45/1.81 tff(51,plain,
% 2.45/1.81 (![V_z: $i, V_S: $i, V_L: $i] : (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[50, 46])).
% 2.45/1.81 tff(52,plain,(
% 2.45/1.81 ![V_z: $i, V_S: $i, V_L: $i] : (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.45/1.81 inference(skolemize,[status(sab)],[51])).
% 2.45/1.81 tff(53,plain,
% 2.45/1.81 (![V_z: $i, V_S: $i, V_L: $i] : (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[52, 45])).
% 2.45/1.81 tff(54,plain,
% 2.45/1.81 (((~![V_z: $i, V_S: $i, V_L: $i] : (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | (c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(v_S, v_r, v_b), v_b, t_a, t_a), v_r, tc_prod(t_a, t_a))))) <=> ((~![V_z: $i, V_S: $i, V_L: $i] : (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(v_S, v_r, v_b), v_b, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.45/1.81 inference(rewrite,[status(thm)],[])).
% 2.45/1.81 tff(55,plain,
% 2.45/1.81 ((~![V_z: $i, V_S: $i, V_L: $i] : (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | (c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(v_S, v_r, v_b), v_b, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.45/1.81 inference(quant_inst,[status(thm)],[])).
% 2.45/1.81 tff(56,plain,
% 2.45/1.81 ((~![V_z: $i, V_S: $i, V_L: $i] : (c_in(c_Pair(V_L, V_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(V_z, v_A, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(V_S, v_r, V_z), V_z, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_b, v_A, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)) | (~c_in(c_Pair(v_sko__4mi(v_S, v_r, v_b), v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[55, 54])).
% 2.45/1.81 tff(57,plain,
% 2.45/1.81 ($false),
% 2.45/1.81 inference(unit_resolution,[status(thm)],[56, 53, 7, 4, 1, 43])).
% 2.45/1.81 tff(58,plain,(c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a))), inference(lemma,lemma(discharge,[]))).
% 2.45/1.81 tff(59,plain,
% 2.45/1.81 ((~c_in(v_L, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), t_a)) <=> (~c_in(v_L, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), t_a))),
% 2.45/1.81 inference(rewrite,[status(thm)],[])).
% 2.45/1.81 tff(60,axiom,(~c_in(v_L, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_6')).
% 2.45/1.81 tff(61,plain,
% 2.45/1.81 (~c_in(v_L, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), t_a)),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[60, 59])).
% 2.45/1.81 tff(62,plain,
% 2.45/1.81 (^[V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : refl((c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))) <=> (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))))),
% 2.45/1.81 inference(bind,[status(th)],[])).
% 2.45/1.81 tff(63,plain,
% 2.45/1.81 (![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))) <=> ![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))),
% 2.45/1.81 inference(quant_intro,[status(thm)],[62])).
% 2.45/1.81 tff(64,plain,
% 2.45/1.81 (![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))) <=> ![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))),
% 2.45/1.81 inference(rewrite,[status(thm)],[])).
% 2.45/1.81 tff(65,plain,
% 2.45/1.81 (^[V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : trans(monotonicity(rewrite(((~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)))) <=> ((~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))), ((((~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)))) | c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a)) <=> (((~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))) | c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a)))), rewrite((((~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a)))) | c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a)) <=> (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))), ((((~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)))) | c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a)) <=> (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))))),
% 2.45/1.81 inference(bind,[status(th)],[])).
% 2.45/1.81 tff(66,plain,
% 2.45/1.81 (![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (((~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)))) | c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a)) <=> ![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))),
% 2.45/1.81 inference(quant_intro,[status(thm)],[65])).
% 2.45/1.81 tff(67,axiom,(![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (((~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)))) | c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0')).
% 2.45/1.81 tff(68,plain,
% 2.45/1.81 (![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[67, 66])).
% 2.45/1.81 tff(69,plain,
% 2.45/1.81 (![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[68, 64])).
% 2.45/1.81 tff(70,plain,(
% 2.45/1.81 ![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))),
% 2.45/1.81 inference(skolemize,[status(sab)],[69])).
% 2.45/1.81 tff(71,plain,
% 2.45/1.81 (![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[70, 63])).
% 2.45/1.81 tff(72,plain,
% 2.45/1.81 (((~![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))) | (c_in(v_L, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), t_a) | (~c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a))))) <=> ((~![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))) | c_in(v_L, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), t_a) | (~c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.45/1.81 inference(rewrite,[status(thm)],[])).
% 2.45/1.81 tff(73,plain,
% 2.45/1.81 ((~![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))) | (c_in(v_L, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), t_a) | (~c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.45/1.81 inference(quant_inst,[status(thm)],[])).
% 2.45/1.81 tff(74,plain,
% 2.45/1.81 ((~![V_x: $i, V_r: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(V_x, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), T_a) | (~c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) | (~c_in(c_Pair(V_x, V_b, T_a, T_a), V_r, tc_prod(T_a, T_a))))) | c_in(v_L, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), t_a) | (~c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[73, 72])).
% 2.45/1.81 tff(75,plain,
% 2.45/1.81 ((~c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_L, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 2.45/1.81 inference(unit_resolution,[status(thm)],[74, 71, 61])).
% 2.45/1.81 tff(76,plain,
% 2.45/1.81 (~c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 2.45/1.81 inference(unit_resolution,[status(thm)],[75, 58])).
% 2.45/1.81 tff(77,assumption,(~c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))), introduced(assumption)).
% 2.45/1.81 tff(78,assumption,(~c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a)), introduced(assumption)).
% 2.45/1.81 tff(79,plain,
% 2.45/1.81 ((~(v_S = c_emptyset)) <=> (~(v_S = c_emptyset))),
% 2.45/1.81 inference(rewrite,[status(thm)],[])).
% 2.45/1.81 tff(80,axiom,(~(v_S = c_emptyset)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 2.45/1.81 tff(81,plain,
% 2.45/1.81 (~(v_S = c_emptyset)),
% 2.45/1.81 inference(modus_ponens,[status(thm)],[80, 79])).
% 2.45/1.81 tff(82,plain,
% 2.45/1.81 (^[V_S: $i, V_a: $i, V_L: $i, V_A: $i] : refl(((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) <=> ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a)))))),
% 2.45/1.81 inference(bind,[status(th)],[])).
% 2.45/1.81 tff(83,plain,
% 2.45/1.81 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) <=> ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))),
% 2.45/1.81 inference(quant_intro,[status(thm)],[82])).
% 2.45/1.81 tff(84,plain,
% 2.45/1.81 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) <=> ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))),
% 2.45/1.81 inference(rewrite,[status(thm)],[])).
% 2.45/1.81 tff(85,plain,
% 2.45/1.81 (^[V_S: $i, V_a: $i, V_L: $i, V_A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c_lessequals(V_S, V_A, tc_set(t_a))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) <=> (c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))), (((((~c_lessequals(V_S, V_A, tc_set(t_a))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) <=> ((c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)))), rewrite(((c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) <=> (c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))), (((((~c_lessequals(V_S, V_A, tc_set(t_a))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) <=> (c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a)))))), ((((((~c_lessequals(V_S, V_A, tc_set(t_a))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) | (V_S = c_emptyset)) <=> ((c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | (V_S = c_emptyset)))), rewrite(((c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | (V_S = c_emptyset)) <=> ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))), ((((((~c_lessequals(V_S, V_A, tc_set(t_a))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) | (V_S = c_emptyset)) <=> ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))))),
% 2.45/1.81 inference(bind,[status(th)],[])).
% 2.45/1.81 tff(86,plain,
% 2.45/1.81 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : (((((~c_lessequals(V_S, V_A, tc_set(t_a))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) | (V_S = c_emptyset)) <=> ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))),
% 2.45/1.81 inference(quant_intro,[status(thm)],[85])).
% 2.45/1.81 tff(87,axiom,(![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : (((((~c_lessequals(V_S, V_A, tc_set(t_a))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) | (V_S = c_emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0')).
% 2.45/1.82 tff(88,plain,
% 2.45/1.82 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[87, 86])).
% 2.45/1.82 tff(89,plain,
% 2.45/1.82 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[88, 84])).
% 2.45/1.82 tff(90,plain,(
% 2.45/1.82 ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))),
% 2.45/1.82 inference(skolemize,[status(sab)],[89])).
% 2.45/1.82 tff(91,plain,
% 2.45/1.82 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[90, 83])).
% 2.45/1.82 tff(92,plain,
% 2.45/1.82 (((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))) | ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a))) <=> ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))) | (v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(93,plain,
% 2.45/1.82 (((v_S = c_emptyset) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)))) <=> ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a))),
% 2.45/1.82 inference(rewrite,[status(thm)],[])).
% 2.45/1.82 tff(94,plain,
% 2.45/1.82 (((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))) | ((v_S = c_emptyset) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))))) <=> ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))) | ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a)))),
% 2.45/1.82 inference(monotonicity,[status(thm)],[93])).
% 2.45/1.82 tff(95,plain,
% 2.45/1.82 (((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))) | ((v_S = c_emptyset) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))))) <=> ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))) | (v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a))),
% 2.45/1.82 inference(transitivity,[status(thm)],[94, 92])).
% 2.45/1.82 tff(96,plain,
% 2.45/1.82 ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))) | ((v_S = c_emptyset) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))))),
% 2.45/1.82 inference(quant_inst,[status(thm)],[])).
% 2.45/1.82 tff(97,plain,
% 2.45/1.82 ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))))) | (v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a)),
% 2.45/1.82 inference(modus_ponens,[status(thm)],[96, 95])).
% 2.45/1.82 tff(98,plain,
% 2.45/1.82 (c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[97, 91, 28, 81])).
% 2.45/1.82 tff(99,plain,
% 2.45/1.82 (c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a)),
% 2.45/1.82 inference(unit_resolution,[status(thm)],[98, 78, 77])).
% 2.45/1.82 tff(100,plain,
% 2.45/1.82 (^[V_S: $i, V_a: $i, V_L: $i, V_A: $i] : refl(((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))))),
% 2.45/1.82 inference(bind,[status(th)],[])).
% 2.45/1.82 tff(101,plain,
% 2.45/1.82 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.45/1.82 inference(quant_intro,[status(thm)],[100])).
% 2.45/1.82 tff(102,plain,
% 2.45/1.82 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.82 inference(rewrite,[status(thm)],[])).
% 2.46/1.82 tff(103,plain,
% 2.46/1.82 (^[V_S: $i, V_a: $i, V_L: $i, V_A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) <=> ((~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))), ((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (((~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))), rewrite((((~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))), ((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))))), (((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) <=> ((c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)))), rewrite(((c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) <=> (c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))), (((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) <=> (c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))))), ((((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) | (V_S = c_emptyset)) <=> ((c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (V_S = c_emptyset)))), rewrite(((c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (V_S = c_emptyset)) <=> ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))), ((((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) | (V_S = c_emptyset)) <=> ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))))),
% 2.46/1.82 inference(bind,[status(th)],[])).
% 2.46/1.82 tff(104,plain,
% 2.46/1.82 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : (((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) | (V_S = c_emptyset)) <=> ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.82 inference(quant_intro,[status(thm)],[103])).
% 2.46/1.82 tff(105,axiom,(![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : (((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a)) | (V_S = c_emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2')).
% 2.46/1.82 tff(106,plain,
% 2.46/1.82 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.82 inference(modus_ponens,[status(thm)],[105, 104])).
% 2.46/1.82 tff(107,plain,
% 2.46/1.82 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.82 inference(modus_ponens,[status(thm)],[106, 102])).
% 2.46/1.82 tff(108,plain,(
% 2.46/1.82 ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.82 inference(skolemize,[status(sab)],[107])).
% 2.46/1.82 tff(109,plain,
% 2.46/1.82 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.82 inference(modus_ponens,[status(thm)],[108, 101])).
% 2.46/1.82 tff(110,plain,
% 2.46/1.82 (((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) <=> ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | (v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.82 inference(rewrite,[status(thm)],[])).
% 2.46/1.82 tff(111,plain,
% 2.46/1.82 (((v_S = c_emptyset) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.82 inference(rewrite,[status(thm)],[])).
% 2.46/1.82 tff(112,plain,
% 2.46/1.82 (((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) <=> ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))))),
% 2.46/1.82 inference(monotonicity,[status(thm)],[111])).
% 2.46/1.82 tff(113,plain,
% 2.46/1.82 (((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) <=> ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | (v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.82 inference(transitivity,[status(thm)],[112, 110])).
% 2.46/1.82 tff(114,plain,
% 2.46/1.82 ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.82 inference(quant_inst,[status(thm)],[])).
% 2.46/1.82 tff(115,plain,
% 2.46/1.82 ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mk(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | (v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 2.46/1.82 inference(modus_ponens,[status(thm)],[114, 113])).
% 2.46/1.82 tff(116,plain,
% 2.46/1.82 (c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[115, 109, 28, 81, 77])).
% 2.46/1.83 tff(117,plain,
% 2.46/1.83 (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[116, 78])).
% 2.46/1.83 tff(118,plain,
% 2.46/1.83 (^[V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : refl((c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a))) <=> (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a))))),
% 2.46/1.83 inference(bind,[status(th)],[])).
% 2.46/1.83 tff(119,plain,
% 2.46/1.83 (![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a))) <=> ![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))),
% 2.46/1.83 inference(quant_intro,[status(thm)],[118])).
% 2.46/1.83 tff(120,plain,
% 2.46/1.83 (![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a))) <=> ![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))),
% 2.46/1.83 inference(rewrite,[status(thm)],[])).
% 2.46/1.83 tff(121,plain,
% 2.46/1.83 (^[V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : rewrite((((~c_in(V_x, V_S, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a)))) | c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) <=> (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a))))),
% 2.46/1.83 inference(bind,[status(th)],[])).
% 2.46/1.83 tff(122,plain,
% 2.46/1.83 (![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (((~c_in(V_x, V_S, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a)))) | c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a))) <=> ![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))),
% 2.46/1.83 inference(quant_intro,[status(thm)],[121])).
% 2.46/1.83 tff(123,axiom,(![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (((~c_in(V_x, V_S, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a)))) | c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0')).
% 2.46/1.83 tff(124,plain,
% 2.46/1.83 (![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))),
% 2.46/1.83 inference(modus_ponens,[status(thm)],[123, 122])).
% 2.46/1.83 tff(125,plain,
% 2.46/1.83 (![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))),
% 2.46/1.83 inference(modus_ponens,[status(thm)],[124, 120])).
% 2.46/1.83 tff(126,plain,(
% 2.46/1.83 ![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))),
% 2.46/1.83 inference(skolemize,[status(sab)],[125])).
% 2.46/1.83 tff(127,plain,
% 2.46/1.83 (![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))),
% 2.46/1.83 inference(modus_ponens,[status(thm)],[126, 119])).
% 2.46/1.83 tff(128,plain,
% 2.46/1.83 (((~![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))) | ((~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a)))) <=> ((~![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a)))),
% 2.46/1.83 inference(rewrite,[status(thm)],[])).
% 2.46/1.83 tff(129,plain,
% 2.46/1.83 ((c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a))) <=> ((~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a)))),
% 2.46/1.83 inference(rewrite,[status(thm)],[])).
% 2.46/1.83 tff(130,plain,
% 2.46/1.83 (((~![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))) | (c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a)))) <=> ((~![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))) | ((~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a))))),
% 2.46/1.83 inference(monotonicity,[status(thm)],[129])).
% 2.46/1.83 tff(131,plain,
% 2.46/1.83 (((~![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))) | (c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a)))) <=> ((~![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a)))),
% 2.46/1.83 inference(transitivity,[status(thm)],[130, 128])).
% 2.46/1.83 tff(132,plain,
% 2.46/1.83 ((~![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))) | (c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a)))),
% 2.46/1.83 inference(quant_inst,[status(thm)],[])).
% 2.46/1.83 tff(133,plain,
% 2.46/1.83 ((~![V_x: $i, V_r: $i, V_S: $i, V_b: $i, V_a: $i, T_a: $i] : (c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a))) | (~c_in(V_x, V_S, T_a)))) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a))),
% 2.46/1.83 inference(modus_ponens,[status(thm)],[132, 131])).
% 2.46/1.83 tff(134,plain,
% 2.46/1.83 (c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[133, 127, 28])).
% 2.46/1.83 tff(135,plain,
% 2.46/1.83 ($false),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[134, 117, 99])).
% 2.46/1.83 tff(136,plain,(c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))), inference(lemma,lemma(discharge,[]))).
% 2.46/1.83 tff(137,plain,
% 2.46/1.83 (c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a)),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[136, 76])).
% 2.46/1.83 tff(138,plain,
% 2.46/1.83 (^[V_S: $i, V_L: $i, V_y: $i] : refl(((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) <=> ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))))),
% 2.46/1.83 inference(bind,[status(th)],[])).
% 2.46/1.83 tff(139,plain,
% 2.46/1.83 (![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) <=> ![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.46/1.83 inference(quant_intro,[status(thm)],[138])).
% 2.46/1.83 tff(140,plain,
% 2.46/1.83 (![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) <=> ![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.46/1.83 inference(rewrite,[status(thm)],[])).
% 2.46/1.83 tff(141,plain,
% 2.46/1.83 (^[V_S: $i, V_L: $i, V_y: $i] : trans(monotonicity(rewrite(((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_y, V_S, t_a))) <=> ((~c_in(V_y, V_S, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))), ((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_y, V_S, t_a))) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (((~c_in(V_y, V_S, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))), rewrite((((~c_in(V_y, V_S, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a))) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))), ((((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_y, V_S, t_a))) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))))),
% 2.46/1.83 inference(bind,[status(th)],[])).
% 2.46/1.83 tff(142,plain,
% 2.46/1.83 (![V_S: $i, V_L: $i, V_y: $i] : (((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_y, V_S, t_a))) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> ![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.46/1.83 inference(quant_intro,[status(thm)],[141])).
% 2.46/1.83 tff(143,axiom,(![V_S: $i, V_L: $i, V_y: $i] : (((~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)) | (~c_in(V_y, V_S, t_a))) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0')).
% 2.46/1.83 tff(144,plain,
% 2.46/1.83 (![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.46/1.83 inference(modus_ponens,[status(thm)],[143, 142])).
% 2.46/1.83 tff(145,plain,
% 2.46/1.83 (![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.46/1.83 inference(modus_ponens,[status(thm)],[144, 140])).
% 2.46/1.83 tff(146,plain,(
% 2.46/1.83 ![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.46/1.83 inference(skolemize,[status(sab)],[145])).
% 2.46/1.83 tff(147,plain,
% 2.46/1.83 (![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))),
% 2.46/1.83 inference(modus_ponens,[status(thm)],[146, 139])).
% 2.46/1.83 tff(148,plain,
% 2.46/1.83 (((~![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | (c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))) <=> ((~![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))),
% 2.46/1.83 inference(rewrite,[status(thm)],[])).
% 2.46/1.83 tff(149,plain,
% 2.46/1.83 (((~c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a)) | c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a))) <=> (c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))),
% 2.46/1.83 inference(rewrite,[status(thm)],[])).
% 2.46/1.83 tff(150,plain,
% 2.46/1.83 (((~![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | ((~c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a)) | c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))) <=> ((~![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | (c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a))))),
% 2.46/1.83 inference(monotonicity,[status(thm)],[149])).
% 2.46/1.83 tff(151,plain,
% 2.46/1.83 (((~![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | ((~c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a)) | c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))) <=> ((~![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))),
% 2.46/1.83 inference(transitivity,[status(thm)],[150, 148])).
% 2.46/1.83 tff(152,plain,
% 2.46/1.83 ((~![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | ((~c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a)) | c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a)))),
% 2.46/1.83 inference(quant_inst,[status(thm)],[])).
% 2.46/1.83 tff(153,plain,
% 2.46/1.83 ((~![V_S: $i, V_L: $i, V_y: $i] : ((~c_in(V_y, V_S, t_a)) | c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_Tarski_OisLub(V_S, v_cl, V_L, t_a)))) | c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a)) | (~c_Tarski_OisLub(v_S, v_cl, v_L, t_a))),
% 2.46/1.83 inference(modus_ponens,[status(thm)],[152, 151])).
% 2.46/1.83 tff(154,plain,
% 2.46/1.83 (c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_sko__4mk(v_L, v_S, v_r), v_S, t_a))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[153, 147, 4])).
% 2.46/1.83 tff(155,plain,
% 2.46/1.83 (c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 2.46/1.83 inference(unit_resolution,[status(thm)],[154, 137])).
% 2.46/1.83 tff(156,plain,
% 2.46/1.83 (^[V_S: $i, V_a: $i, V_L: $i, V_A: $i] : refl(((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))))),
% 2.46/1.83 inference(bind,[status(th)],[])).
% 2.46/1.83 tff(157,plain,
% 2.46/1.83 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.83 inference(quant_intro,[status(thm)],[156])).
% 2.46/1.83 tff(158,plain,
% 2.46/1.83 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.83 inference(rewrite,[status(thm)],[])).
% 2.46/1.83 tff(159,plain,
% 2.46/1.83 (^[V_S: $i, V_a: $i, V_L: $i, V_A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) <=> ((~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))), ((((~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (((~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))), rewrite((((~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))), ((((~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))))), (((((~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) <=> ((c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)))), rewrite(((c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) <=> (c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))), (((((~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) <=> (c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))))), ((((((~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) | (V_S = c_emptyset)) <=> ((c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (V_S = c_emptyset)))), rewrite(((c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (V_S = c_emptyset)) <=> ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))), ((((((~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) | (V_S = c_emptyset)) <=> ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))))),
% 2.46/1.83 inference(bind,[status(th)],[])).
% 2.46/1.83 tff(160,plain,
% 2.46/1.83 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : (((((~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) | (V_S = c_emptyset)) <=> ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(quant_intro,[status(thm)],[159])).
% 2.46/1.84 tff(161,axiom,(![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : (((((~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a)) | (V_S = c_emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1')).
% 2.46/1.84 tff(162,plain,
% 2.46/1.84 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(modus_ponens,[status(thm)],[161, 160])).
% 2.46/1.84 tff(163,plain,
% 2.46/1.84 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(modus_ponens,[status(thm)],[162, 158])).
% 2.46/1.84 tff(164,plain,(
% 2.46/1.84 ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(skolemize,[status(sab)],[163])).
% 2.46/1.84 tff(165,plain,
% 2.46/1.84 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(modus_ponens,[status(thm)],[164, 157])).
% 2.46/1.84 tff(166,plain,
% 2.46/1.84 (((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) <=> ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | (v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(rewrite,[status(thm)],[])).
% 2.46/1.84 tff(167,plain,
% 2.46/1.84 (((v_S = c_emptyset) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(rewrite,[status(thm)],[])).
% 2.46/1.84 tff(168,plain,
% 2.46/1.84 (((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) <=> ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))))),
% 2.46/1.84 inference(monotonicity,[status(thm)],[167])).
% 2.46/1.84 tff(169,plain,
% 2.46/1.84 (((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) <=> ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | (v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(transitivity,[status(thm)],[168, 166])).
% 2.46/1.84 tff(170,plain,
% 2.46/1.84 ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(quant_inst,[status(thm)],[])).
% 2.46/1.84 tff(171,plain,
% 2.46/1.84 ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(v_sko__4mj(V_S, V_a, v_r), V_S, t_a) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | (v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 2.46/1.84 inference(modus_ponens,[status(thm)],[170, 169])).
% 2.46/1.84 tff(172,plain,
% 2.46/1.84 (c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[171, 165, 28, 81])).
% 2.46/1.84 tff(173,plain,
% 2.46/1.84 (c_in(v_sko__4mj(v_S, v_a, v_r), v_S, t_a)),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[172, 155, 76])).
% 2.46/1.84 tff(174,plain,
% 2.46/1.84 (c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 2.46/1.84 inference(unit_resolution,[status(thm)],[134, 173])).
% 2.46/1.84 tff(175,plain,
% 2.46/1.84 (^[V_S: $i, V_a: $i, V_L: $i, V_A: $i] : refl(((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))))),
% 2.46/1.84 inference(bind,[status(th)],[])).
% 2.46/1.84 tff(176,plain,
% 2.46/1.84 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(quant_intro,[status(thm)],[175])).
% 2.46/1.84 tff(177,plain,
% 2.46/1.84 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(rewrite,[status(thm)],[])).
% 2.46/1.84 tff(178,plain,
% 2.46/1.84 (^[V_S: $i, V_a: $i, V_L: $i, V_A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ((~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))), ((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) <=> (((~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))))), rewrite((((~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) <=> ((~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))), ((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) <=> ((~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))))), (((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (((~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))), rewrite((((~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))), (((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))))), ((((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (V_S = c_emptyset)) <=> ((c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (V_S = c_emptyset)))), rewrite(((c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (V_S = c_emptyset)) <=> ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))), ((((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (V_S = c_emptyset)) <=> ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))))),
% 2.46/1.84 inference(bind,[status(th)],[])).
% 2.46/1.84 tff(179,plain,
% 2.46/1.84 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : (((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (V_S = c_emptyset)) <=> ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(quant_intro,[status(thm)],[178])).
% 2.46/1.84 tff(180,axiom,(![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : (((((~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, V_A, tc_set(t_a)))) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (V_S = c_emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3')).
% 2.46/1.84 tff(181,plain,
% 2.46/1.84 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(modus_ponens,[status(thm)],[180, 179])).
% 2.46/1.84 tff(182,plain,
% 2.46/1.84 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(modus_ponens,[status(thm)],[181, 177])).
% 2.46/1.84 tff(183,plain,(
% 2.46/1.84 ![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(skolemize,[status(sab)],[182])).
% 2.46/1.84 tff(184,plain,
% 2.46/1.84 (![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(modus_ponens,[status(thm)],[183, 176])).
% 2.46/1.84 tff(185,plain,
% 2.46/1.84 (((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) <=> ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | (v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.84 inference(rewrite,[status(thm)],[])).
% 2.46/1.84 tff(186,plain,
% 2.46/1.84 (((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.85 inference(rewrite,[status(thm)],[])).
% 2.46/1.85 tff(187,plain,
% 2.46/1.85 (((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) <=> ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))))),
% 2.46/1.85 inference(monotonicity,[status(thm)],[186])).
% 2.46/1.85 tff(188,plain,
% 2.46/1.85 (((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) <=> ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | (v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.85 inference(transitivity,[status(thm)],[187, 185])).
% 2.46/1.85 tff(189,plain,
% 2.46/1.85 ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | ((v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 2.46/1.85 inference(quant_inst,[status(thm)],[])).
% 2.46/1.85 tff(190,plain,
% 2.46/1.85 ((~![V_S: $i, V_a: $i, V_L: $i, V_A: $i] : ((V_S = c_emptyset) | c_in(c_Pair(V_a, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, V_A, tc_set(t_a))) | (~c_in(c_Pair(v_sko__4mk(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(V_a, v_sko__4mj(V_S, V_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))))) | (v_S = c_emptyset) | c_in(c_Pair(v_a, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a))) | (~c_in(c_Pair(v_a, v_sko__4mj(v_S, v_a, v_r), t_a, t_a), v_r, tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_sko__4mk(v_L, v_S, v_r), v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 2.46/1.85 inference(modus_ponens,[status(thm)],[189, 188])).
% 2.46/1.85 tff(191,plain,
% 2.46/1.85 ($false),
% 2.46/1.85 inference(unit_resolution,[status(thm)],[190, 184, 28, 81, 76, 155, 174])).
% 2.46/1.85 % SZS output end Proof
%------------------------------------------------------------------------------