TSTP Solution File: SET831-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET831-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 : Tue Sep 20 05:08:13 EDT 2022
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET831-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 08:11:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(c_in_type, type, (
% 0.20/0.39 c_in: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(t_a_type, type, (
% 0.20/0.39 t_a: $i)).
% 0.20/0.39 tff(v_Z_type, type, (
% 0.20/0.39 v_Z: $i)).
% 0.20/0.39 tff(c_Main_OsubsetI__1_type, type, (
% 0.20/0.39 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(c_inter_type, type, (
% 0.20/0.39 c_inter: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(v_Y_type, type, (
% 0.20/0.39 v_Y: $i)).
% 0.20/0.39 tff(v_x_type, type, (
% 0.20/0.39 v_x: $i)).
% 0.20/0.39 tff(c_lessequals_type, type, (
% 0.20/0.39 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(tc_set_type, type, (
% 0.20/0.39 tc_set: $i > $i)).
% 0.20/0.39 tff(v_X_type, type, (
% 0.20/0.39 v_X: $i)).
% 0.20/0.39 tff(1,assumption,(~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)), introduced(assumption)).
% 0.20/0.39 tff(2,assumption,(~(v_X = c_inter(v_Y, v_Z, t_a))), introduced(assumption)).
% 0.20/0.39 tff(3,assumption,(~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))), introduced(assumption)).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (^[T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(7,axiom,(![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetI_1')).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.39 tff(9,plain,(
% 0.20/0.39 ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[8])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (^[T_a: $i, V_B: $i, V_A: $i] : refl((c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(18,axiom,(![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetI_0')).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.40 tff(20,plain,(
% 0.20/0.40 ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[19])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 ((c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) <=> (c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a))),
% 0.20/0.40 inference(transitivity,[status(thm)],[24, 22])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[27, 21, 3])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a)) <=> ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), 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, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), 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, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(32,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OIntE_1')).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.40 tff(34,plain,(
% 0.20/0.40 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))),
% 0.20/0.40 inference(skolemize,[status(sab)],[33])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))) | ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))) | ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_A, T_a))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Y, t_a), v_Y, t_a)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[38, 35, 28, 14])).
% 0.20/0.40 tff(40,plain,(c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(41,assumption,(~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))), introduced(assumption)).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[44, 10])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[45, 41])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[49, 21])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[50, 41])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) <=> ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), 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, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), 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, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(55,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OIntE_0')).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.40 tff(57,plain,(
% 0.20/0.40 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))),
% 0.20/0.41 inference(skolemize,[status(sab)],[56])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))) | ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))) | ((~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a))) | (~c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_inter(v_Y, v_Z, t_a), v_Z, t_a), v_Z, t_a)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[61, 58, 51, 46])).
% 0.20/0.41 tff(63,plain,(c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (^[V_U: $i] : refl(((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a))) <=> ![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a))) <=> ![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (^[V_U: $i] : trans(monotonicity(rewrite((((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a)))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))), (((((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a)))) | (~c_lessequals(V_U, v_Y, tc_set(t_a)))) <=> (((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Y, tc_set(t_a)))))), rewrite((((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Y, tc_set(t_a)))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))), (((((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a)))) | (~c_lessequals(V_U, v_Y, tc_set(t_a)))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (![V_U: $i] : ((((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a)))) | (~c_lessequals(V_U, v_Y, tc_set(t_a)))) <=> ![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.41 tff(69,axiom,(![V_U: $i] : ((((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(V_U, v_X, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a)))) | (~c_lessequals(V_U, v_Y, tc_set(t_a))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_5')).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.41 tff(72,plain,(
% 0.20/0.41 ![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[71])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))))) <=> ((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)))) <=> ((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)))) <=> ((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 ((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~![V_U: $i] : ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(V_U, v_Y, tc_set(t_a))) | (~c_lessequals(V_U, v_Z, tc_set(t_a))) | c_lessequals(V_U, v_X, tc_set(t_a)))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[79, 73, 63])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 ((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[80, 40])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[81, 2])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (^[T_a: $i, V_B: $i, V_A: $i] : refl(((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (^[T_a: $i, V_B: $i, V_A: $i] : trans(monotonicity(rewrite(((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) <=> ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))), ((((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> (((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | (V_A = V_B)))), rewrite((((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | (V_A = V_B)) <=> ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))), ((((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (![T_a: $i, V_B: $i, V_A: $i] : (((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.42 tff(88,axiom,(![T_a: $i, V_B: $i, V_A: $i] : (((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_Osubset__antisym_0')).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.20/0.42 tff(91,plain,(
% 0.20/0.42 ![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[90])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (((~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[94])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[95, 93])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (V_A = V_B) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (v_X = c_inter(v_Y, v_Z, t_a)) | (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) | (~c_lessequals(c_inter(v_Y, v_Z, t_a), v_X, tc_set(t_a)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (~c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[98, 2, 92, 82])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 ((c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))) <=> (c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[101])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))),
% 0.20/0.43 inference(transitivity,[status(thm)],[102, 100])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[105, 21, 99])).
% 0.20/0.43 tff(107,assumption,(~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)), introduced(assumption)).
% 0.20/0.43 tff(108,assumption,(c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)), introduced(assumption)).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_c, V_B, T_a) | (~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_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(110,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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, 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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.43 tff(111,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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, 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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (^[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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (![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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.43 tff(114,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')).
% 0.20/0.43 tff(115,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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.43 tff(116,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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.20/0.43 tff(117,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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[116])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.20/0.43 tff(119,assumption,(~c_lessequals(v_X, v_Z, tc_set(t_a))), introduced(assumption)).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Z, tc_set(t_a))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Z, tc_set(t_a)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(121,axiom,((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Z, tc_set(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 ((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Z, tc_set(t_a))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 (v_X = c_inter(v_Y, v_Z, t_a)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[122, 119])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (c_lessequals(v_X, v_Z, tc_set(t_a)) <=> c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[123])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 (c_lessequals(c_inter(v_Y, v_Z, t_a), v_Z, tc_set(t_a)) <=> c_lessequals(v_X, v_Z, tc_set(t_a))),
% 0.20/0.43 inference(symmetry,[status(thm)],[124])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 (c_lessequals(v_X, v_Z, tc_set(t_a))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[63, 125])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[119, 126])).
% 0.20/0.43 tff(128,plain,(c_lessequals(v_X, v_Z, tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(129,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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 ((c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(131,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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Z, 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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[130])).
% 0.20/0.43 tff(132,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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Z, 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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[131, 129])).
% 0.20/0.43 tff(133,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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[134, 128, 118, 108, 107])).
% 0.20/0.43 tff(136,plain,(c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[136, 106])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_X, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[140, 10, 99])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a))) <=> (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, 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, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[142])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, 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, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : trans(monotonicity(rewrite(((~c_in(V_c, V_B, T_a)) | (~c_in(V_c, V_A, T_a))) <=> ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))), ((((~c_in(V_c, V_B, T_a)) | (~c_in(V_c, V_A, T_a))) | c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) <=> (((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a))) | c_in(V_c, c_inter(V_A, V_B, T_a), T_a)))), rewrite((((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a))) | c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) <=> (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))), ((((~c_in(V_c, V_B, T_a)) | (~c_in(V_c, V_A, T_a))) | c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) <=> (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_B, T_a)) | (~c_in(V_c, V_A, T_a))) | c_in(V_c, c_inter(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[145])).
% 0.20/0.44 tff(147,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_B, T_a)) | (~c_in(V_c, V_A, T_a))) | c_in(V_c, c_inter(V_A, V_B, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OIntI_0')).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.20/0.44 tff(150,plain,(
% 0.20/0.44 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[149])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 ((~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[154, 151, 141])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[155, 137])).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 (((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Y, tc_set(t_a))) <=> ((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Y, tc_set(t_a)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(158,axiom,((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Y, tc_set(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 ((v_X = c_inter(v_Y, v_Z, t_a)) | c_lessequals(v_X, v_Y, tc_set(t_a))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 (c_lessequals(v_X, v_Y, tc_set(t_a))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[159, 2])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 ((c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Y, 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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[162])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Y, 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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[163, 161])).
% 0.20/0.44 tff(165,plain,
% 0.20/0.44 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a)) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_X, c_inter(v_Y, v_Z, t_a), t_a), v_X, t_a))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[166, 160, 118, 106, 156])).
% 0.20/0.44 tff(168,plain,(v_X = c_inter(v_Y, v_Z, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(169,plain,
% 0.20/0.44 (c_inter(v_Y, v_Z, t_a) = v_X),
% 0.20/0.44 inference(symmetry,[status(thm)],[168])).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 (c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)) <=> c_lessequals(v_x, v_X, tc_set(t_a))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[169])).
% 0.20/0.44 tff(171,plain,
% 0.20/0.44 (c_lessequals(v_x, v_X, tc_set(t_a)) <=> c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.20/0.44 inference(symmetry,[status(thm)],[170])).
% 0.20/0.44 tff(172,plain,
% 0.20/0.44 ((~c_lessequals(v_x, v_X, tc_set(t_a))) <=> (~c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[171])).
% 0.20/0.44 tff(173,plain,
% 0.20/0.44 (c_lessequals(v_X, v_Y, tc_set(t_a)) <=> c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[168])).
% 0.20/0.44 tff(174,plain,
% 0.20/0.44 (c_lessequals(c_inter(v_Y, v_Z, t_a), v_Y, tc_set(t_a)) <=> c_lessequals(v_X, v_Y, tc_set(t_a))),
% 0.20/0.44 inference(symmetry,[status(thm)],[173])).
% 0.20/0.44 tff(175,plain,
% 0.20/0.44 (c_lessequals(v_X, v_Y, tc_set(t_a))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[40, 174])).
% 0.20/0.44 tff(176,plain,
% 0.20/0.44 (((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(177,plain,
% 0.20/0.44 ((((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(178,plain,
% 0.20/0.44 ((((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(179,plain,
% 0.20/0.44 (((~c_lessequals(v_x, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(180,plain,
% 0.20/0.44 ((((~c_lessequals(v_x, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> (((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.45 tff(181,plain,
% 0.20/0.45 ((((~c_lessequals(v_x, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[180, 178])).
% 0.20/0.45 tff(182,plain,
% 0.20/0.45 (((((~c_lessequals(v_x, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> (((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[181])).
% 0.20/0.45 tff(183,plain,
% 0.20/0.45 (((((~c_lessequals(v_x, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[182, 177])).
% 0.20/0.45 tff(184,axiom,((((~c_lessequals(v_x, v_X, tc_set(t_a))) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.20/0.45 tff(185,plain,
% 0.20/0.45 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.20/0.45 tff(186,plain,
% 0.20/0.45 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[185, 176])).
% 0.20/0.45 tff(187,plain,
% 0.20/0.45 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[186, 176])).
% 0.20/0.45 tff(188,plain,
% 0.20/0.45 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[187, 176])).
% 0.20/0.45 tff(189,plain,
% 0.20/0.45 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[188, 176])).
% 0.20/0.45 tff(190,plain,
% 0.20/0.45 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[189, 176])).
% 0.20/0.45 tff(191,plain,
% 0.20/0.45 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[190, 176])).
% 0.20/0.45 tff(192,plain,
% 0.20/0.45 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | (~c_lessequals(v_x, v_X, tc_set(t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[191, 176])).
% 0.20/0.45 tff(193,plain,
% 0.20/0.45 (~c_lessequals(v_x, v_X, tc_set(t_a))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[192, 175, 128, 168])).
% 0.20/0.45 tff(194,plain,
% 0.20/0.45 (~c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[193, 172])).
% 0.20/0.45 tff(195,plain,
% 0.20/0.45 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(196,plain,
% 0.20/0.45 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(197,plain,
% 0.20/0.45 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.20/0.45 tff(198,plain,
% 0.20/0.45 (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[197, 21])).
% 0.20/0.45 tff(199,plain,
% 0.20/0.45 (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[198, 194])).
% 0.20/0.45 tff(200,plain,
% 0.20/0.45 ((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(201,plain,
% 0.20/0.45 (((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(202,plain,
% 0.20/0.45 (((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(203,plain,
% 0.20/0.45 ((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) <=> (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(204,plain,
% 0.20/0.45 (((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> ((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[203])).
% 0.20/0.45 tff(205,plain,
% 0.20/0.45 (((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[204, 202])).
% 0.20/0.45 tff(206,plain,
% 0.20/0.45 ((((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> ((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[205])).
% 0.20/0.45 tff(207,plain,
% 0.20/0.45 ((((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[206, 201])).
% 0.20/0.45 tff(208,axiom,(((c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.20/0.45 tff(209,plain,
% 0.20/0.45 (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.20/0.45 tff(210,plain,
% 0.20/0.45 (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[209, 200])).
% 0.20/0.45 tff(211,plain,
% 0.20/0.45 (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[210, 200])).
% 0.20/0.45 tff(212,plain,
% 0.20/0.45 (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[211, 200])).
% 0.20/0.45 tff(213,plain,
% 0.20/0.45 (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[212, 200])).
% 0.20/0.45 tff(214,plain,
% 0.20/0.45 (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[213, 200])).
% 0.20/0.45 tff(215,plain,
% 0.20/0.45 (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[214, 200])).
% 0.20/0.45 tff(216,plain,
% 0.20/0.45 (c_lessequals(v_x, v_Y, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[215, 200])).
% 0.20/0.45 tff(217,plain,
% 0.20/0.45 (c_lessequals(v_x, v_Y, tc_set(t_a))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[216, 175, 128, 168])).
% 0.20/0.45 tff(218,plain,
% 0.20/0.45 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_x, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_x, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(219,plain,
% 0.20/0.45 ((c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Y, tc_set(t_a)))) <=> ((~c_lessequals(v_x, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(220,plain,
% 0.20/0.46 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Y, 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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_x, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[219])).
% 0.20/0.46 tff(221,plain,
% 0.20/0.46 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Y, 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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_x, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[220, 218])).
% 0.20/0.46 tff(222,plain,
% 0.20/0.46 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Y, tc_set(t_a))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(223,plain,
% 0.20/0.46 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_x, v_Y, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.20/0.46 tff(224,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[223, 217, 118, 199, 1])).
% 0.20/0.46 tff(225,plain,(c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(226,plain,
% 0.20/0.46 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(227,plain,
% 0.20/0.46 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(228,plain,
% 0.20/0.46 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.20/0.46 tff(229,plain,
% 0.20/0.46 ((~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)) | c_lessequals(v_x, c_inter(v_Y, v_Z, t_a), tc_set(t_a))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[228, 10])).
% 0.20/0.46 tff(230,plain,
% 0.20/0.46 (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[229, 194])).
% 0.20/0.46 tff(231,plain,
% 0.20/0.46 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(232,plain,
% 0.20/0.46 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(233,plain,
% 0.20/0.46 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, c_inter(V_A, V_B, T_a), T_a) | (~c_in(V_c, V_A, T_a)) | (~c_in(V_c, V_B, T_a)))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), c_inter(v_Y, v_Z, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.20/0.46 tff(234,plain,
% 0.20/0.46 ((~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Y, t_a)) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[233, 151, 230])).
% 0.20/0.46 tff(235,plain,
% 0.20/0.46 (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[234, 225])).
% 0.20/0.46 tff(236,plain,
% 0.20/0.46 (((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(237,plain,
% 0.20/0.46 ((((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(238,plain,
% 0.20/0.46 ((((~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(239,plain,
% 0.20/0.46 ((c_lessequals(v_x, v_Z, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(240,plain,
% 0.20/0.46 (((c_lessequals(v_x, v_Z, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> (((~c_lessequals(v_X, v_Z, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[239])).
% 0.20/0.46 tff(241,plain,
% 0.20/0.46 (((c_lessequals(v_x, v_Z, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[240, 238])).
% 0.20/0.46 tff(242,plain,
% 0.20/0.46 ((((c_lessequals(v_x, v_Z, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> (((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[241])).
% 0.20/0.46 tff(243,plain,
% 0.20/0.46 ((((c_lessequals(v_x, v_Z, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))) <=> ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[242, 237])).
% 0.20/0.46 tff(244,axiom,(((c_lessequals(v_x, v_Z, tc_set(t_a)) | (~c_lessequals(v_X, v_Z, tc_set(t_a)))) | (~c_lessequals(v_X, v_Y, tc_set(t_a)))) | (~(v_X = c_inter(v_Y, v_Z, t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.20/0.46 tff(245,plain,
% 0.20/0.46 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.20/0.46 tff(246,plain,
% 0.20/0.46 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[245, 236])).
% 0.20/0.46 tff(247,plain,
% 0.20/0.46 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[246, 236])).
% 0.20/0.46 tff(248,plain,
% 0.20/0.46 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[247, 236])).
% 0.20/0.46 tff(249,plain,
% 0.20/0.46 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[248, 236])).
% 0.20/0.46 tff(250,plain,
% 0.20/0.46 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[249, 236])).
% 0.20/0.46 tff(251,plain,
% 0.20/0.46 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[250, 236])).
% 0.20/0.46 tff(252,plain,
% 0.20/0.46 ((~c_lessequals(v_X, v_Z, tc_set(t_a))) | (~c_lessequals(v_X, v_Y, tc_set(t_a))) | (~(v_X = c_inter(v_Y, v_Z, t_a))) | c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[251, 236])).
% 0.20/0.46 tff(253,plain,
% 0.20/0.46 (c_lessequals(v_x, v_Z, tc_set(t_a))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[252, 175, 128, 168])).
% 0.20/0.46 tff(254,plain,
% 0.20/0.46 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_x, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_x, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(255,plain,
% 0.20/0.46 ((c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Z, tc_set(t_a)))) <=> ((~c_lessequals(v_x, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(256,plain,
% 0.20/0.46 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Z, 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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | ((~c_lessequals(v_x, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[255])).
% 0.20/0.47 tff(257,plain,
% 0.20/0.47 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Z, 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_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_x, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[256, 254])).
% 0.20/0.47 tff(258,plain,
% 0.20/0.47 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a)) | (~c_lessequals(v_x, v_Z, tc_set(t_a))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(259,plain,
% 0.20/0.47 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | (~c_lessequals(v_x, v_Z, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_Z, t_a) | (~c_in(c_Main_OsubsetI__1(v_x, c_inter(v_Y, v_Z, t_a), t_a), v_x, t_a))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.20/0.47 tff(260,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[259, 253, 118, 199, 235])).
% 0.20/0.47 % SZS output end Proof
%------------------------------------------------------------------------------