TSTP Solution File: SET860-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET860-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 05:08:26 EDT 2022
% Result : Unsatisfiable 4.98s 3.52s
% Output : Proof 5.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET860-2 : TPTP v8.1.0. Released v3.2.0.
% 0.14/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 08:24:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 4.98/3.52 % SZS status Unsatisfiable
% 4.98/3.52 % SZS output start Proof
% 4.98/3.52 tff(c_lessequals_type, type, (
% 4.98/3.52 c_lessequals: ( $i * $i * $i ) > $o)).
% 4.98/3.52 tff(tc_set_type, type, (
% 4.98/3.52 tc_set: $i > $i)).
% 4.98/3.52 tff(t_a_type, type, (
% 4.98/3.52 t_a: $i)).
% 4.98/3.52 tff(v_A_type, type, (
% 4.98/3.52 v_A: $i)).
% 4.98/3.52 tff(c_Main_OUnionE__1_type, type, (
% 4.98/3.52 c_Main_OUnionE__1: ( $i * $i * $i ) > $i)).
% 4.98/3.52 tff(v_C_type, type, (
% 4.98/3.52 v_C: $i)).
% 4.98/3.52 tff(c_Main_OsubsetI__1_type, type, (
% 4.98/3.52 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 4.98/3.52 tff(c_Union_type, type, (
% 4.98/3.52 c_Union: ( $i * $i ) > $i)).
% 4.98/3.52 tff(v_B_type, type, (
% 4.98/3.52 v_B: $i)).
% 4.98/3.52 tff(c_in_type, type, (
% 4.98/3.52 c_in: ( $i * $i * $i ) > $o)).
% 4.98/3.52 tff(1,assumption,(~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))), introduced(assumption)).
% 4.98/3.52 tff(2,assumption,(c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)), introduced(assumption)).
% 4.98/3.52 tff(3,plain,
% 4.98/3.52 (^[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))))),
% 4.98/3.52 inference(bind,[status(th)],[])).
% 4.98/3.52 tff(4,plain,
% 4.98/3.52 (![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)))),
% 4.98/3.52 inference(quant_intro,[status(thm)],[3])).
% 4.98/3.52 tff(5,plain,
% 4.98/3.52 (![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)))),
% 4.98/3.52 inference(rewrite,[status(thm)],[])).
% 4.98/3.52 tff(6,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')).
% 4.98/3.52 tff(7,plain,
% 4.98/3.52 (![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)))),
% 4.98/3.52 inference(modus_ponens,[status(thm)],[6, 5])).
% 4.98/3.52 tff(8,plain,(
% 4.98/3.52 ![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)))),
% 4.98/3.52 inference(skolemize,[status(sab)],[7])).
% 4.98/3.52 tff(9,plain,
% 4.98/3.52 (![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)))),
% 4.98/3.52 inference(modus_ponens,[status(thm)],[8, 4])).
% 4.98/3.52 tff(10,plain,
% 4.98/3.52 ((~c_lessequals(c_Union(v_C, t_a), v_A, tc_set(t_a))) <=> (~c_lessequals(c_Union(v_C, t_a), v_A, tc_set(t_a)))),
% 4.98/3.52 inference(rewrite,[status(thm)],[])).
% 4.98/3.52 tff(11,axiom,(~c_lessequals(c_Union(v_C, t_a), v_A, tc_set(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 4.98/3.52 tff(12,plain,
% 4.98/3.52 (~c_lessequals(c_Union(v_C, t_a), v_A, tc_set(t_a))),
% 4.98/3.52 inference(modus_ponens,[status(thm)],[11, 10])).
% 4.98/3.52 tff(13,plain,
% 4.98/3.52 (((~![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_Union(v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, 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_Union(v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a))),
% 4.98/3.52 inference(rewrite,[status(thm)],[])).
% 4.98/3.52 tff(14,plain,
% 4.98/3.52 ((c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | c_lessequals(c_Union(v_C, t_a), v_A, tc_set(t_a))) <=> (c_lessequals(c_Union(v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a))),
% 4.98/3.53 inference(rewrite,[status(thm)],[])).
% 4.98/3.53 tff(15,plain,
% 4.98/3.53 (((~![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_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | c_lessequals(c_Union(v_C, t_a), v_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(c_Union(v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)))),
% 4.98/3.53 inference(monotonicity,[status(thm)],[14])).
% 4.98/3.53 tff(16,plain,
% 4.98/3.53 (((~![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_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | c_lessequals(c_Union(v_C, t_a), v_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(c_Union(v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a))),
% 4.98/3.53 inference(transitivity,[status(thm)],[15, 13])).
% 4.98/3.53 tff(17,plain,
% 4.98/3.53 ((~![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_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | c_lessequals(c_Union(v_C, t_a), v_A, tc_set(t_a)))),
% 4.98/3.53 inference(quant_inst,[status(thm)],[])).
% 4.98/3.53 tff(18,plain,
% 4.98/3.53 ((~![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_Union(v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)),
% 4.98/3.53 inference(modus_ponens,[status(thm)],[17, 16])).
% 4.98/3.53 tff(19,plain,
% 4.98/3.53 (c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)),
% 4.98/3.53 inference(unit_resolution,[status(thm)],[18, 12, 9])).
% 4.98/3.53 tff(20,plain,
% 4.98/3.53 (^[T_a: $i, V_A: $i, V_C: $i] : refl(((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a)) <=> ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a)))),
% 4.98/3.53 inference(bind,[status(th)],[])).
% 4.98/3.53 tff(21,plain,
% 4.98/3.53 (![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a)) <=> ![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))),
% 4.98/3.53 inference(quant_intro,[status(thm)],[20])).
% 4.98/3.53 tff(22,plain,
% 4.98/3.53 (![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a)) <=> ![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))),
% 4.98/3.53 inference(rewrite,[status(thm)],[])).
% 4.98/3.53 tff(23,axiom,(![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUnionE_1')).
% 4.98/3.53 tff(24,plain,
% 4.98/3.53 (![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))),
% 4.98/3.53 inference(modus_ponens,[status(thm)],[23, 22])).
% 4.98/3.53 tff(25,plain,(
% 4.98/3.53 ![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))),
% 4.98/3.53 inference(skolemize,[status(sab)],[24])).
% 4.98/3.53 tff(26,plain,
% 4.98/3.53 (![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))),
% 4.98/3.53 inference(modus_ponens,[status(thm)],[25, 21])).
% 4.98/3.53 tff(27,plain,
% 4.98/3.53 (((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a))) <=> ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 4.98/3.53 inference(rewrite,[status(thm)],[])).
% 4.98/3.53 tff(28,plain,
% 4.98/3.53 ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 4.98/3.53 inference(quant_inst,[status(thm)],[])).
% 4.98/3.53 tff(29,plain,
% 4.98/3.53 ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)),
% 4.98/3.53 inference(modus_ponens,[status(thm)],[28, 27])).
% 4.98/3.53 tff(30,plain,
% 4.98/3.53 (c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)),
% 4.98/3.53 inference(unit_resolution,[status(thm)],[29, 26, 19])).
% 4.98/3.53 tff(31,plain,
% 4.98/3.53 (^[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))))),
% 4.98/3.53 inference(bind,[status(th)],[])).
% 4.98/3.53 tff(32,plain,
% 4.98/3.53 (![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)))),
% 4.98/3.53 inference(quant_intro,[status(thm)],[31])).
% 4.98/3.53 tff(33,plain,
% 4.98/3.53 (![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)))),
% 4.98/3.53 inference(rewrite,[status(thm)],[])).
% 4.98/3.53 tff(34,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')).
% 4.98/3.53 tff(35,plain,
% 4.98/3.53 (![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)))),
% 4.98/3.53 inference(modus_ponens,[status(thm)],[34, 33])).
% 4.98/3.53 tff(36,plain,(
% 4.98/3.53 ![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)))),
% 4.98/3.53 inference(skolemize,[status(sab)],[35])).
% 4.98/3.53 tff(37,plain,
% 4.98/3.53 (![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)))),
% 4.98/3.53 inference(modus_ponens,[status(thm)],[36, 32])).
% 4.98/3.53 tff(38,plain,
% 4.98/3.53 (((~![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_Union(v_C, t_a), v_A, t_a), v_A, t_a)) | c_lessequals(c_Union(v_C, t_a), v_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(c_Union(v_C, t_a), v_A, t_a), v_A, t_a)) | c_lessequals(c_Union(v_C, t_a), v_A, tc_set(t_a)))),
% 4.98/3.53 inference(rewrite,[status(thm)],[])).
% 4.98/3.53 tff(39,plain,
% 4.98/3.53 ((~![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_Union(v_C, t_a), v_A, t_a), v_A, t_a)) | c_lessequals(c_Union(v_C, t_a), v_A, tc_set(t_a)))),
% 4.98/3.53 inference(quant_inst,[status(thm)],[])).
% 4.98/3.53 tff(40,plain,
% 4.98/3.53 ((~![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_Union(v_C, t_a), v_A, t_a), v_A, t_a)) | c_lessequals(c_Union(v_C, t_a), v_A, tc_set(t_a))),
% 4.98/3.53 inference(modus_ponens,[status(thm)],[39, 38])).
% 4.98/3.53 tff(41,plain,
% 4.98/3.53 (~c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_A, t_a)),
% 4.98/3.53 inference(unit_resolution,[status(thm)],[40, 12, 37])).
% 4.98/3.53 tff(42,plain,
% 4.98/3.53 (^[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)))))),
% 4.98/3.53 inference(bind,[status(th)],[])).
% 4.98/3.53 tff(43,plain,
% 4.98/3.53 (![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))))),
% 4.98/3.53 inference(quant_intro,[status(thm)],[42])).
% 4.98/3.53 tff(44,plain,
% 4.98/3.53 (![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))))),
% 4.98/3.53 inference(rewrite,[status(thm)],[])).
% 4.98/3.53 tff(45,plain,
% 4.98/3.53 (^[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)))))),
% 4.98/3.53 inference(bind,[status(th)],[])).
% 4.98/3.53 tff(46,plain,
% 4.98/3.53 (![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))))),
% 4.98/3.53 inference(quant_intro,[status(thm)],[45])).
% 4.98/3.53 tff(47,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')).
% 4.98/3.53 tff(48,plain,
% 4.98/3.53 (![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))))),
% 4.98/3.53 inference(modus_ponens,[status(thm)],[47, 46])).
% 4.98/3.53 tff(49,plain,
% 4.98/3.53 (![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))))),
% 4.98/3.53 inference(modus_ponens,[status(thm)],[48, 44])).
% 4.98/3.53 tff(50,plain,(
% 4.98/3.53 ![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))))),
% 4.98/3.53 inference(skolemize,[status(sab)],[49])).
% 4.98/3.53 tff(51,plain,
% 4.98/3.53 (![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))))),
% 4.98/3.53 inference(modus_ponens,[status(thm)],[50, 43])).
% 4.98/3.53 tff(52,plain,
% 4.98/3.53 (((~![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(c_Union(v_C, t_a), v_A, t_a), v_A, t_a) | (~c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)) | (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, 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_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_A, t_a) | (~c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)) | (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))))),
% 4.98/3.53 inference(rewrite,[status(thm)],[])).
% 5.11/3.53 tff(53,plain,
% 5.11/3.53 ((~![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(c_Union(v_C, t_a), v_A, t_a), v_A, t_a) | (~c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)) | (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))))),
% 5.11/3.53 inference(quant_inst,[status(thm)],[])).
% 5.11/3.53 tff(54,plain,
% 5.11/3.53 ((~![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(c_Union(v_C, t_a), v_A, t_a), v_A, t_a) | (~c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)) | (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)))),
% 5.11/3.53 inference(modus_ponens,[status(thm)],[53, 52])).
% 5.11/3.53 tff(55,plain,
% 5.11/3.53 (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))),
% 5.11/3.53 inference(unit_resolution,[status(thm)],[54, 51, 41, 30])).
% 5.11/3.53 tff(56,plain,
% 5.11/3.53 (((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, 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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.53 inference(rewrite,[status(thm)],[])).
% 5.11/3.53 tff(57,plain,
% 5.11/3.53 ((c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))) <=> (c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.53 inference(rewrite,[status(thm)],[])).
% 5.11/3.53 tff(58,plain,
% 5.11/3.53 (((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_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(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)))),
% 5.11/3.53 inference(monotonicity,[status(thm)],[57])).
% 5.11/3.53 tff(59,plain,
% 5.11/3.53 (((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_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(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.53 inference(transitivity,[status(thm)],[58, 56])).
% 5.11/3.53 tff(60,plain,
% 5.11/3.53 ((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)))),
% 5.11/3.53 inference(quant_inst,[status(thm)],[])).
% 5.11/3.53 tff(61,plain,
% 5.11/3.53 ((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)),
% 5.11/3.53 inference(modus_ponens,[status(thm)],[60, 59])).
% 5.11/3.53 tff(62,plain,
% 5.11/3.53 (c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)),
% 5.11/3.53 inference(unit_resolution,[status(thm)],[61, 9, 55])).
% 5.11/3.53 tff(63,plain,
% 5.11/3.53 (^[T_a: $i, V_A: $i, V_C: $i] : refl(((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a))) <=> ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a))))),
% 5.11/3.53 inference(bind,[status(th)],[])).
% 5.11/3.53 tff(64,plain,
% 5.11/3.53 (![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a))) <=> ![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))),
% 5.11/3.53 inference(quant_intro,[status(thm)],[63])).
% 5.11/3.53 tff(65,plain,
% 5.11/3.53 (![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a))) <=> ![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))),
% 5.11/3.53 inference(rewrite,[status(thm)],[])).
% 5.11/3.53 tff(66,axiom,(![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUnionE_0')).
% 5.11/3.53 tff(67,plain,
% 5.11/3.53 (![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))),
% 5.11/3.53 inference(modus_ponens,[status(thm)],[66, 65])).
% 5.11/3.53 tff(68,plain,(
% 5.11/3.53 ![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))),
% 5.11/3.53 inference(skolemize,[status(sab)],[67])).
% 5.11/3.53 tff(69,plain,
% 5.11/3.53 (![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))),
% 5.11/3.53 inference(modus_ponens,[status(thm)],[68, 64])).
% 5.11/3.53 tff(70,plain,
% 5.11/3.53 (((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a)))) <=> ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a)))),
% 5.11/3.53 inference(rewrite,[status(thm)],[])).
% 5.11/3.53 tff(71,plain,
% 5.11/3.53 ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a)))),
% 5.11/3.53 inference(quant_inst,[status(thm)],[])).
% 5.11/3.53 tff(72,plain,
% 5.11/3.53 ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))),
% 5.11/3.53 inference(modus_ponens,[status(thm)],[71, 70])).
% 5.11/3.53 tff(73,plain,
% 5.11/3.53 (c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))),
% 5.11/3.53 inference(unit_resolution,[status(thm)],[72, 69, 19])).
% 5.11/3.53 tff(74,plain,
% 5.11/3.53 (^[T_a: $i, V_X: $i, V_A: $i, V_C: $i] : refl((c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a))) <=> (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a))))),
% 5.11/3.53 inference(bind,[status(th)],[])).
% 5.11/3.53 tff(75,plain,
% 5.11/3.53 (![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a))) <=> ![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 5.11/3.53 inference(quant_intro,[status(thm)],[74])).
% 5.11/3.53 tff(76,plain,
% 5.11/3.53 (![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a))) <=> ![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 5.11/3.53 inference(rewrite,[status(thm)],[])).
% 5.11/3.53 tff(77,plain,
% 5.11/3.53 (^[T_a: $i, V_X: $i, V_A: $i, V_C: $i] : rewrite((((~c_in(V_A, V_X, T_a)) | (~c_in(V_X, V_C, tc_set(T_a)))) | c_in(V_A, c_Union(V_C, T_a), T_a)) <=> (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a))))),
% 5.11/3.53 inference(bind,[status(th)],[])).
% 5.11/3.53 tff(78,plain,
% 5.11/3.53 (![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (((~c_in(V_A, V_X, T_a)) | (~c_in(V_X, V_C, tc_set(T_a)))) | c_in(V_A, c_Union(V_C, T_a), T_a)) <=> ![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 5.11/3.53 inference(quant_intro,[status(thm)],[77])).
% 5.11/3.53 tff(79,axiom,(![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (((~c_in(V_A, V_X, T_a)) | (~c_in(V_X, V_C, tc_set(T_a)))) | c_in(V_A, c_Union(V_C, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUnionI_0')).
% 5.11/3.53 tff(80,plain,
% 5.11/3.53 (![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 5.11/3.53 inference(modus_ponens,[status(thm)],[79, 78])).
% 5.11/3.53 tff(81,plain,
% 5.11/3.53 (![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 5.11/3.53 inference(modus_ponens,[status(thm)],[80, 76])).
% 5.11/3.53 tff(82,plain,(
% 5.11/3.53 ![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 5.11/3.53 inference(skolemize,[status(sab)],[81])).
% 5.11/3.53 tff(83,plain,
% 5.11/3.53 (![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))),
% 5.11/3.53 inference(modus_ponens,[status(thm)],[82, 75])).
% 5.11/3.53 tff(84,plain,
% 5.11/3.53 (((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | ((~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)))) <=> ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)))),
% 5.11/3.53 inference(rewrite,[status(thm)],[])).
% 5.11/3.53 tff(85,plain,
% 5.11/3.53 ((c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a))) <=> ((~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)))),
% 5.11/3.53 inference(rewrite,[status(thm)],[])).
% 5.11/3.53 tff(86,plain,
% 5.11/3.53 (((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)))) <=> ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | ((~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a))))),
% 5.11/3.53 inference(monotonicity,[status(thm)],[85])).
% 5.11/3.53 tff(87,plain,
% 5.11/3.53 (((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)))) <=> ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)))),
% 5.11/3.54 inference(transitivity,[status(thm)],[86, 84])).
% 5.11/3.54 tff(88,plain,
% 5.11/3.54 ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a)))),
% 5.11/3.54 inference(quant_inst,[status(thm)],[])).
% 5.11/3.54 tff(89,plain,
% 5.11/3.54 ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.54 inference(modus_ponens,[status(thm)],[88, 87])).
% 5.11/3.54 tff(90,plain,
% 5.11/3.54 (c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)),
% 5.11/3.54 inference(unit_resolution,[status(thm)],[89, 83, 73, 62])).
% 5.11/3.54 tff(91,plain,
% 5.11/3.54 (((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))) <=> ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.54 inference(rewrite,[status(thm)],[])).
% 5.11/3.54 tff(92,plain,
% 5.11/3.54 ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.54 inference(quant_inst,[status(thm)],[])).
% 5.11/3.54 tff(93,plain,
% 5.11/3.54 ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)),
% 5.11/3.54 inference(modus_ponens,[status(thm)],[92, 91])).
% 5.11/3.54 tff(94,plain,
% 5.11/3.54 (c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)),
% 5.11/3.54 inference(unit_resolution,[status(thm)],[93, 26, 90])).
% 5.11/3.54 tff(95,plain,
% 5.11/3.54 (((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a)) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_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(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a)) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)))),
% 5.11/3.54 inference(rewrite,[status(thm)],[])).
% 5.11/3.54 tff(96,plain,
% 5.11/3.54 ((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a)) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)))),
% 5.11/3.54 inference(quant_inst,[status(thm)],[])).
% 5.11/3.54 tff(97,plain,
% 5.11/3.54 ((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a)) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))),
% 5.11/3.54 inference(modus_ponens,[status(thm)],[96, 95])).
% 5.11/3.54 tff(98,plain,
% 5.11/3.54 (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a)),
% 5.11/3.54 inference(unit_resolution,[status(thm)],[97, 37, 55])).
% 5.11/3.54 tff(99,plain,
% 5.11/3.54 (((~![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(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)) | (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, 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_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)) | (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))))),
% 5.11/3.54 inference(rewrite,[status(thm)],[])).
% 5.11/3.54 tff(100,plain,
% 5.11/3.54 ((~![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(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)) | (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))))),
% 5.11/3.54 inference(quant_inst,[status(thm)],[])).
% 5.11/3.54 tff(101,plain,
% 5.11/3.54 ((~![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(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)) | (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)))),
% 5.11/3.54 inference(modus_ponens,[status(thm)],[100, 99])).
% 5.11/3.54 tff(102,plain,
% 5.11/3.54 (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))),
% 5.11/3.54 inference(unit_resolution,[status(thm)],[101, 51, 98, 94])).
% 5.11/3.54 tff(103,plain,
% 5.11/3.54 (((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, 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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.54 inference(rewrite,[status(thm)],[])).
% 5.11/3.54 tff(104,plain,
% 5.11/3.54 ((c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))) <=> (c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.54 inference(rewrite,[status(thm)],[])).
% 5.11/3.54 tff(105,plain,
% 5.11/3.54 (((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_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(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)))),
% 5.11/3.54 inference(monotonicity,[status(thm)],[104])).
% 5.11/3.54 tff(106,plain,
% 5.11/3.54 (((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_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(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.54 inference(transitivity,[status(thm)],[105, 103])).
% 5.11/3.54 tff(107,plain,
% 5.11/3.54 ((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)))),
% 5.11/3.54 inference(quant_inst,[status(thm)],[])).
% 5.11/3.54 tff(108,plain,
% 5.11/3.54 ((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)),
% 5.11/3.54 inference(modus_ponens,[status(thm)],[107, 106])).
% 5.11/3.54 tff(109,plain,
% 5.11/3.54 (c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)),
% 5.11/3.54 inference(unit_resolution,[status(thm)],[108, 9, 102])).
% 5.11/3.54 tff(110,plain,
% 5.11/3.54 (((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a)))) <=> ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a)))),
% 5.11/3.54 inference(rewrite,[status(thm)],[])).
% 5.11/3.54 tff(111,plain,
% 5.11/3.54 ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a)))),
% 5.11/3.54 inference(quant_inst,[status(thm)],[])).
% 5.11/3.54 tff(112,plain,
% 5.11/3.54 ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))),
% 5.11/3.54 inference(modus_ponens,[status(thm)],[111, 110])).
% 5.11/3.54 tff(113,plain,
% 5.11/3.54 (c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))),
% 5.11/3.54 inference(unit_resolution,[status(thm)],[112, 69, 90])).
% 5.11/3.54 tff(114,plain,
% 5.11/3.54 (((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | ((~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)))) <=> ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)))),
% 5.11/3.54 inference(rewrite,[status(thm)],[])).
% 5.11/3.54 tff(115,plain,
% 5.11/3.54 ((c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))) <=> ((~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)))),
% 5.11/3.55 inference(rewrite,[status(thm)],[])).
% 5.11/3.55 tff(116,plain,
% 5.11/3.55 (((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)))) <=> ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | ((~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))))),
% 5.11/3.55 inference(monotonicity,[status(thm)],[115])).
% 5.11/3.55 tff(117,plain,
% 5.11/3.55 (((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)))) <=> ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)))),
% 5.11/3.55 inference(transitivity,[status(thm)],[116, 114])).
% 5.11/3.55 tff(118,plain,
% 5.11/3.55 ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)))),
% 5.11/3.55 inference(quant_inst,[status(thm)],[])).
% 5.11/3.55 tff(119,plain,
% 5.11/3.55 ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.55 inference(modus_ponens,[status(thm)],[118, 117])).
% 5.11/3.55 tff(120,plain,
% 5.11/3.55 (c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)),
% 5.11/3.55 inference(unit_resolution,[status(thm)],[119, 83, 113, 109])).
% 5.11/3.55 tff(121,plain,
% 5.11/3.55 (((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a)))) <=> ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a)))),
% 5.11/3.55 inference(rewrite,[status(thm)],[])).
% 5.11/3.55 tff(122,plain,
% 5.11/3.55 ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a)))),
% 5.11/3.55 inference(quant_inst,[status(thm)],[])).
% 5.11/3.55 tff(123,plain,
% 5.11/3.55 ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(c_Main_OUnionE__1(V_A, V_C, T_a), V_C, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))),
% 5.11/3.55 inference(modus_ponens,[status(thm)],[122, 121])).
% 5.11/3.55 tff(124,plain,
% 5.11/3.55 (c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))),
% 5.11/3.55 inference(unit_resolution,[status(thm)],[123, 69, 120])).
% 5.11/3.55 tff(125,plain,
% 5.11/3.55 ((~c_lessequals(v_B, c_Union(v_C, t_a), tc_set(t_a))) <=> (~c_lessequals(v_B, c_Union(v_C, t_a), tc_set(t_a)))),
% 5.11/3.55 inference(rewrite,[status(thm)],[])).
% 5.11/3.55 tff(126,axiom,(~c_lessequals(v_B, c_Union(v_C, t_a), tc_set(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 5.11/3.55 tff(127,plain,
% 5.11/3.55 (~c_lessequals(v_B, c_Union(v_C, t_a), tc_set(t_a))),
% 5.11/3.55 inference(modus_ponens,[status(thm)],[126, 125])).
% 5.11/3.55 tff(128,plain,
% 5.11/3.55 (((~![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_B, c_Union(v_C, t_a), t_a), c_Union(v_C, t_a), t_a)) | c_lessequals(v_B, c_Union(v_C, 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_B, c_Union(v_C, t_a), t_a), c_Union(v_C, t_a), t_a)) | c_lessequals(v_B, c_Union(v_C, t_a), tc_set(t_a)))),
% 5.11/3.55 inference(rewrite,[status(thm)],[])).
% 5.11/3.55 tff(129,plain,
% 5.11/3.55 ((~![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_B, c_Union(v_C, t_a), t_a), c_Union(v_C, t_a), t_a)) | c_lessequals(v_B, c_Union(v_C, t_a), tc_set(t_a)))),
% 5.11/3.55 inference(quant_inst,[status(thm)],[])).
% 5.11/3.55 tff(130,plain,
% 5.11/3.55 ((~![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_B, c_Union(v_C, t_a), t_a), c_Union(v_C, t_a), t_a)) | c_lessequals(v_B, c_Union(v_C, t_a), tc_set(t_a))),
% 5.11/3.55 inference(modus_ponens,[status(thm)],[129, 128])).
% 5.11/3.55 tff(131,plain,
% 5.11/3.55 (~c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Union(v_C, t_a), t_a)),
% 5.11/3.55 inference(unit_resolution,[status(thm)],[130, 127, 37])).
% 5.11/3.55 tff(132,plain,
% 5.11/3.55 (((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)))) <=> ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)))),
% 5.11/3.55 inference(rewrite,[status(thm)],[])).
% 5.11/3.55 tff(133,plain,
% 5.11/3.55 ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | (c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)))),
% 5.11/3.55 inference(quant_inst,[status(thm)],[])).
% 5.11/3.55 tff(134,plain,
% 5.11/3.55 ((~![T_a: $i, V_X: $i, V_A: $i, V_C: $i] : (c_in(V_A, c_Union(V_C, T_a), T_a) | (~c_in(V_X, V_C, tc_set(T_a))) | (~c_in(V_A, V_X, T_a)))) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Union(v_C, t_a), t_a) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | (~c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.55 inference(modus_ponens,[status(thm)],[133, 132])).
% 5.11/3.55 tff(135,plain,
% 5.11/3.55 ($false),
% 5.11/3.55 inference(unit_resolution,[status(thm)],[134, 83, 131, 124, 2])).
% 5.11/3.55 tff(136,plain,(~c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)), inference(lemma,lemma(discharge,[]))).
% 5.11/3.55 tff(137,plain,
% 5.11/3.55 (((~![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_B, c_Union(v_C, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, 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_B, c_Union(v_C, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a))),
% 5.11/3.55 inference(rewrite,[status(thm)],[])).
% 5.11/3.55 tff(138,plain,
% 5.11/3.55 ((c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a) | c_lessequals(v_B, c_Union(v_C, t_a), tc_set(t_a))) <=> (c_lessequals(v_B, c_Union(v_C, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a))),
% 5.11/3.55 inference(rewrite,[status(thm)],[])).
% 5.11/3.55 tff(139,plain,
% 5.11/3.55 (((~![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_B, c_Union(v_C, t_a), t_a), v_B, t_a) | c_lessequals(v_B, c_Union(v_C, 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_B, c_Union(v_C, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a)))),
% 5.11/3.55 inference(monotonicity,[status(thm)],[138])).
% 5.11/3.55 tff(140,plain,
% 5.11/3.55 (((~![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_B, c_Union(v_C, t_a), t_a), v_B, t_a) | c_lessequals(v_B, c_Union(v_C, 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_B, c_Union(v_C, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a))),
% 5.11/3.55 inference(transitivity,[status(thm)],[139, 137])).
% 5.11/3.55 tff(141,plain,
% 5.11/3.55 ((~![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_B, c_Union(v_C, t_a), t_a), v_B, t_a) | c_lessequals(v_B, c_Union(v_C, t_a), tc_set(t_a)))),
% 5.11/3.55 inference(quant_inst,[status(thm)],[])).
% 5.11/3.55 tff(142,plain,
% 5.11/3.55 ((~![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_B, c_Union(v_C, t_a), tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a)),
% 5.11/3.55 inference(modus_ponens,[status(thm)],[141, 140])).
% 5.11/3.55 tff(143,plain,
% 5.11/3.55 (c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a)),
% 5.11/3.55 inference(unit_resolution,[status(thm)],[142, 127, 9])).
% 5.11/3.55 tff(144,plain,
% 5.11/3.55 (((~![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_B, c_Union(v_C, t_a), t_a), v_B, t_a)) | (~c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), 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_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a)) | (~c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.55 inference(rewrite,[status(thm)],[])).
% 5.11/3.55 tff(145,plain,
% 5.11/3.55 ((c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a)) | (~c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a)))) <=> ((~c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a)) | (~c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.55 inference(rewrite,[status(thm)],[])).
% 5.11/3.55 tff(146,plain,
% 5.11/3.55 (((~![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_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a)) | (~c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), 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_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a)) | (~c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)))),
% 5.11/3.55 inference(monotonicity,[status(thm)],[145])).
% 5.11/3.55 tff(147,plain,
% 5.11/3.55 (((~![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_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a)) | (~c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), 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_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a)) | (~c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.55 inference(transitivity,[status(thm)],[146, 144])).
% 5.11/3.55 tff(148,plain,
% 5.11/3.55 ((~![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_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a) | (~c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), v_B, t_a)) | (~c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a))))),
% 5.11/3.55 inference(quant_inst,[status(thm)],[])).
% 5.11/3.55 tff(149,plain,
% 5.11/3.55 ((~![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_B, c_Union(v_C, t_a), t_a), v_B, t_a)) | (~c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a))) | c_in(c_Main_OsubsetI__1(v_B, c_Union(v_C, t_a), t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)),
% 5.11/3.56 inference(modus_ponens,[status(thm)],[148, 147])).
% 5.11/3.56 tff(150,plain,
% 5.11/3.56 (~c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a))),
% 5.11/3.56 inference(unit_resolution,[status(thm)],[149, 51, 143, 136])).
% 5.11/3.56 tff(151,plain,
% 5.11/3.56 (^[V_U: $i] : refl(((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a))) <=> ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a))))),
% 5.11/3.56 inference(bind,[status(th)],[])).
% 5.11/3.56 tff(152,plain,
% 5.11/3.56 (![V_U: $i] : ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a))) <=> ![V_U: $i] : ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a)))),
% 5.11/3.56 inference(quant_intro,[status(thm)],[151])).
% 5.11/3.56 tff(153,plain,
% 5.11/3.56 (![V_U: $i] : ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a))) <=> ![V_U: $i] : ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a)))),
% 5.11/3.56 inference(rewrite,[status(thm)],[])).
% 5.11/3.56 tff(154,plain,
% 5.11/3.56 (^[V_U: $i] : rewrite(((c_lessequals(v_B, V_U, tc_set(t_a)) | c_lessequals(V_U, v_A, tc_set(t_a))) | (~c_in(V_U, v_C, tc_set(t_a)))) <=> ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a))))),
% 5.11/3.56 inference(bind,[status(th)],[])).
% 5.11/3.56 tff(155,plain,
% 5.11/3.56 (![V_U: $i] : ((c_lessequals(v_B, V_U, tc_set(t_a)) | c_lessequals(V_U, v_A, tc_set(t_a))) | (~c_in(V_U, v_C, tc_set(t_a)))) <=> ![V_U: $i] : ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a)))),
% 5.11/3.56 inference(quant_intro,[status(thm)],[154])).
% 5.11/3.56 tff(156,axiom,(![V_U: $i] : ((c_lessequals(v_B, V_U, tc_set(t_a)) | c_lessequals(V_U, v_A, tc_set(t_a))) | (~c_in(V_U, v_C, tc_set(t_a))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 5.11/3.56 tff(157,plain,
% 5.11/3.56 (![V_U: $i] : ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a)))),
% 5.11/3.56 inference(modus_ponens,[status(thm)],[156, 155])).
% 5.11/3.56 tff(158,plain,
% 5.11/3.56 (![V_U: $i] : ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a)))),
% 5.11/3.56 inference(modus_ponens,[status(thm)],[157, 153])).
% 5.11/3.56 tff(159,plain,(
% 5.11/3.56 ![V_U: $i] : ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a)))),
% 5.11/3.56 inference(skolemize,[status(sab)],[158])).
% 5.11/3.56 tff(160,plain,
% 5.11/3.56 (![V_U: $i] : ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a)))),
% 5.11/3.56 inference(modus_ponens,[status(thm)],[159, 152])).
% 5.11/3.56 tff(161,plain,
% 5.11/3.56 (((~![V_U: $i] : ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a)))) | ((~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a)))) <=> ((~![V_U: $i] : ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a)))) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a)))),
% 5.11/3.56 inference(rewrite,[status(thm)],[])).
% 5.11/3.56 tff(162,plain,
% 5.11/3.56 ((~![V_U: $i] : ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a)))) | ((~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a)))),
% 5.11/3.56 inference(quant_inst,[status(thm)],[])).
% 5.11/3.56 tff(163,plain,
% 5.11/3.56 ((~![V_U: $i] : ((~c_in(V_U, v_C, tc_set(t_a))) | c_lessequals(V_U, v_A, tc_set(t_a)) | c_lessequals(v_B, V_U, tc_set(t_a)))) | (~c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_C, tc_set(t_a))) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a))),
% 5.11/3.56 inference(modus_ponens,[status(thm)],[162, 161])).
% 5.11/3.56 tff(164,plain,
% 5.11/3.56 (c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)) | c_lessequals(v_B, c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), tc_set(t_a))),
% 5.11/3.56 inference(unit_resolution,[status(thm)],[163, 160, 124])).
% 5.11/3.56 tff(165,plain,
% 5.11/3.56 ($false),
% 5.11/3.56 inference(unit_resolution,[status(thm)],[164, 150, 1])).
% 5.11/3.56 tff(166,plain,(c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 5.11/3.56 tff(167,plain,
% 5.11/3.56 (((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))) <=> ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.56 inference(rewrite,[status(thm)],[])).
% 5.11/3.56 tff(168,plain,
% 5.11/3.56 ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a))),
% 5.11/3.56 inference(quant_inst,[status(thm)],[])).
% 5.11/3.56 tff(169,plain,
% 5.11/3.56 ((~![T_a: $i, V_A: $i, V_C: $i] : ((~c_in(V_A, c_Union(V_C, T_a), T_a)) | c_in(V_A, c_Main_OUnionE__1(V_A, V_C, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Union(v_C, t_a), t_a)) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)),
% 5.11/3.56 inference(modus_ponens,[status(thm)],[168, 167])).
% 5.11/3.56 tff(170,plain,
% 5.11/3.56 (c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)),
% 5.11/3.56 inference(unit_resolution,[status(thm)],[169, 26, 120])).
% 5.11/3.56 tff(171,plain,
% 5.11/3.56 (((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a)) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_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(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a)) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)))),
% 5.11/3.56 inference(rewrite,[status(thm)],[])).
% 5.11/3.56 tff(172,plain,
% 5.11/3.56 ((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a)) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)))),
% 5.11/3.56 inference(quant_inst,[status(thm)],[])).
% 5.11/3.56 tff(173,plain,
% 5.11/3.56 ((~![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_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a)) | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))),
% 5.11/3.56 inference(modus_ponens,[status(thm)],[172, 171])).
% 5.11/3.56 tff(174,plain,
% 5.11/3.56 (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a)),
% 5.11/3.56 inference(unit_resolution,[status(thm)],[173, 37, 102])).
% 5.11/3.56 tff(175,plain,
% 5.11/3.56 (((~![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(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)) | (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, 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_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)) | (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))))),
% 5.11/3.56 inference(rewrite,[status(thm)],[])).
% 5.11/3.56 tff(176,plain,
% 5.11/3.56 ((~![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(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)) | (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a))))),
% 5.11/3.56 inference(quant_inst,[status(thm)],[])).
% 5.11/3.56 tff(177,plain,
% 5.11/3.56 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))))) | c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_A, t_a) | (~c_in(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), t_a)) | (~c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, t_a), v_C, t_a), v_A, tc_set(t_a)))),
% 5.11/3.56 inference(modus_ponens,[status(thm)],[176, 175])).
% 5.11/3.56 tff(178,plain,
% 5.11/3.56 ($false),
% 5.11/3.56 inference(unit_resolution,[status(thm)],[177, 51, 174, 170, 166])).
% 5.11/3.56 % SZS output end Proof
%------------------------------------------------------------------------------