TSTP Solution File: LAT276-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT276-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LAT276-2 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Sep 1 12:57:05 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(c_in_type, type, (
% 0.20/0.40 c_in: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(tc_prod_type, type, (
% 0.20/0.40 tc_prod: ( $i * $i ) > $i)).
% 0.20/0.40 tff(t_a_type, type, (
% 0.20/0.40 t_a: $i)).
% 0.20/0.40 tff(c_Tarski_Opotype_Oorder_type, type, (
% 0.20/0.40 c_Tarski_Opotype_Oorder: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tc_Product__Type_Ounit_type, type, (
% 0.20/0.40 tc_Product__Type_Ounit: $i)).
% 0.20/0.40 tff(v_cl_type, type, (
% 0.20/0.40 v_cl: $i)).
% 0.20/0.40 tff(c_Pair_type, type, (
% 0.20/0.40 c_Pair: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.40 tff(v_xa_type, type, (
% 0.20/0.40 v_xa: $i)).
% 0.20/0.40 tff(v_sko__4mP_type, type, (
% 0.20/0.40 v_sko__4mP: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(v_S_type, type, (
% 0.20/0.40 v_S: $i)).
% 0.20/0.40 tff(c_Tarski_Opotype_Opset_type, type, (
% 0.20/0.40 c_Tarski_Opotype_Opset: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(c_lessequals_type, type, (
% 0.20/0.40 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(tc_set_type, type, (
% 0.20/0.40 tc_set: $i > $i)).
% 0.20/0.40 tff(c_Tarski_Olub_type, type, (
% 0.20/0.40 c_Tarski_Olub: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(v_r_type, type, (
% 0.20/0.40 v_r: $i)).
% 0.20/0.40 tff(v_A_type, type, (
% 0.20/0.40 v_A: $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[V_S: $i, V_L: $i] : refl((c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[V_S: $i, V_L: $i] : trans(monotonicity(rewrite(c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) <=> c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))), rewrite((~c_lessequals(V_S, v_A, tc_set(t_a))) <=> (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)))), rewrite((~c_in(V_L, v_A, t_a)) <=> (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a))), rewrite((~c_in(c_Pair(v_sko__4mP(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__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))), ((c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))))), rewrite((c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))), ((c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (^[V_S: $i, V_L: $i] : trans(monotonicity(rewrite((((~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(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(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))), (((((~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(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(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))), (((((~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(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(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![V_S: $i, V_L: $i] : ((((~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(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(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> ![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.41 tff(8,axiom,(![V_S: $i, V_L: $i] : ((((~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(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(c_Tarski_Olub(V_S, v_cl, t_a), 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_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1')).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.20/0.41 tff(12,plain,(
% 0.20/0.42 ![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[11])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (^[V_x: $i, V_S: $i] : refl(((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)))) <=> ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)))) <=> ![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (^[V_x: $i, V_S: $i] : trans(monotonicity(rewrite(c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) <=> c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))), rewrite((~c_lessequals(V_S, v_A, tc_set(t_a))) <=> (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)))), ((c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), 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_x, V_S, t_a))) <=> (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_x, V_S, t_a))))), rewrite((c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_x, V_S, t_a))) <=> ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))), ((c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), 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_x, V_S, t_a))) <=> ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), 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_x, V_S, t_a))) <=> ![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), 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_x, V_S, t_a))) <=> ![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), 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_x, V_S, t_a)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (^[V_x: $i, V_S: $i] : rewrite((((~c_in(V_x, V_S, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), 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_x, V_S, t_a))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![V_x: $i, V_S: $i] : (((~c_in(V_x, V_S, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> ![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), 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_x, V_S, t_a)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.42 tff(21,axiom,(![V_x: $i, V_S: $i] : (((~c_in(V_x, V_S, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), 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_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0')).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), 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_x, V_S, t_a)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), 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_x, V_S, t_a)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[23, 17])).
% 0.20/0.42 tff(25,plain,(
% 0.20/0.42 ![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[24])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.20/0.42 tff(27,assumption,(~c_in(v_xa, v_S, t_a)), introduced(assumption)).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (((~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(v_xa, v_S, t_a)) <=> ((~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(v_xa, v_S, t_a))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(29,axiom,((~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(v_xa, v_S, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 ((~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(v_xa, v_S, t_a)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[30, 27])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))) <=> (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.42 tff(37,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetD_0')).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.42 tff(40,plain,(
% 0.20/0.42 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[39])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.42 tff(42,assumption,(~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)), introduced(assumption)).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 ((c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)) <=> (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(44,axiom,(c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[45, 43])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[48, 43])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[49, 43])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[51, 43])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[52, 43])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (c_in(v_xa, v_S, t_a)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[53, 42])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (c_lessequals(v_S, v_A, tc_set(t_a)) <=> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (c_lessequals(v_S, v_A, tc_set(t_a)) <=> c_lessequals(v_S, v_A, tc_set(t_a))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(57,axiom,(c_lessequals(v_S, v_A, tc_set(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (c_lessequals(v_S, v_A, tc_set(t_a))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 ((c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, v_S, t_a))) <=> (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, v_S, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, v_S, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[62, 60])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, v_S, t_a)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[65, 59, 42, 54, 41])).
% 0.20/0.43 tff(67,plain,(c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (((~![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))) | (c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))) <=> ((~![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 ((~![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))) | (c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 ((~![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)) | (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[70, 59, 67, 31, 13])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (^[V_S: $i, V_L: $i] : refl((c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a))) <=> (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a))) <=> ![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (^[V_S: $i, V_L: $i] : trans(monotonicity(rewrite(c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) <=> c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a)), rewrite(c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) <=> c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))), rewrite((~c_lessequals(V_S, v_A, tc_set(t_a))) <=> (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)))), rewrite((~c_in(V_L, v_A, t_a)) <=> (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a))), ((c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a))) <=> (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a))))), rewrite((c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a))) <=> (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))), ((c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a))) <=> (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a))) <=> ![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a))) <=> ![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (^[V_S: $i, V_L: $i] : trans(monotonicity(rewrite((((~c_in(V_L, v_A, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)))), (((((~c_in(V_L, v_A, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a)) <=> ((c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a))) | c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a)))), rewrite(((c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a))) | c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a)) <=> (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)))), (((((~c_in(V_L, v_A, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a)) <=> (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (![V_S: $i, V_L: $i] : ((((~c_in(V_L, v_A, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a)) <=> ![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.44 tff(79,axiom,(![V_S: $i, V_L: $i] : ((((~c_in(V_L, v_A, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0')).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_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_L, v_A, t_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[81, 75])).
% 0.20/0.44 tff(83,plain,(
% 0.20/0.44 ![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[82])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (((~![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))) | (c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))) <=> ((~![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 ((c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a))) <=> (c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 (((~![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))) | (c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))) <=> ((~![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))) | (c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[86])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 (((~![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))) | (c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))) <=> ((~![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[87, 85])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 ((~![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))) | (c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 ((~![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(V_L, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)))) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a) | (~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[90, 59, 67, 31, 84])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (^[V_U: $i] : refl((c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> ![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> ![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 (^[V_U: $i] : trans(monotonicity(rewrite((c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_U, v_S, t_a))) <=> ((~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))), (((c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_U, v_S, t_a))) | c_in(v_xa, v_S, t_a)) <=> (((~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(v_xa, v_S, t_a)))), rewrite((((~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(v_xa, v_S, t_a)) <=> (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))), (((c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_U, v_S, t_a))) | c_in(v_xa, v_S, t_a)) <=> (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (![V_U: $i] : ((c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_U, v_S, t_a))) | c_in(v_xa, v_S, t_a)) <=> ![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.46 tff(97,axiom,(![V_U: $i] : ((c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_U, v_S, t_a))) | c_in(v_xa, v_S, t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_9')).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 (![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.20/0.46 tff(100,plain,(
% 0.20/0.46 ![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[99])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (((~![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | (c_in(v_xa, v_S, t_a) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)))) <=> ((~![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | c_in(v_xa, v_S, t_a) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 ((c_in(v_xa, v_S, t_a) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> (c_in(v_xa, v_S, t_a) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 (((~![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | (c_in(v_xa, v_S, t_a) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | (c_in(v_xa, v_S, t_a) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 (((~![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | (c_in(v_xa, v_S, t_a) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | c_in(v_xa, v_S, t_a) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[104, 102])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 ((~![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | (c_in(v_xa, v_S, t_a) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 ((~![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | c_in(v_xa, v_S, t_a) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[107, 27, 101, 91, 71])).
% 0.20/0.47 tff(109,plain,(c_in(v_xa, v_S, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (((~![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))) | (c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))) <=> ((~![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))) | c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (((~c_in(v_xa, v_S, t_a)) | c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)))) <=> (c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 (((~![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))) | ((~c_in(v_xa, v_S, t_a)) | c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))) <=> ((~![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))) | (c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (((~![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))) | ((~c_in(v_xa, v_S, t_a)) | c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))) <=> ((~![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))) | c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[112, 110])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 ((~![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))) | ((~c_in(v_xa, v_S, t_a)) | c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 ((~![V_x: $i, V_S: $i] : ((~c_in(V_x, V_S, t_a)) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_lessequals(V_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))) | c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 (c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[115, 59, 109, 26])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (((~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(119,axiom,((~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_6')).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[120, 117])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[121, 116])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[70, 59, 67, 122, 13])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[90, 59, 67, 122, 84])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (^[V_V: $i] : refl(((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> ![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> ![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (^[V_V: $i] : trans(monotonicity(rewrite((c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_V, v_S, t_a))) <=> ((~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))), (((c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_V, v_S, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> (((~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))))), rewrite((((~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))), (((c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_V, v_S, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 (![V_V: $i] : ((c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_V, v_S, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.48 tff(130,axiom,(![V_V: $i] : ((c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_V, v_S, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_10')).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 (![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.20/0.48 tff(133,plain,(
% 0.20/0.48 ![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[132])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 (![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (((~![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)))) <=> ((~![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 (((~![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[136])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 (((~![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[137, 135])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 ((~![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 ((~![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(v_sko__4mP(v_xa, v_S, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), v_S, t_a))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[140, 134, 116, 124, 123])).
% 0.20/0.48 % SZS output end Proof
%------------------------------------------------------------------------------