TSTP Solution File: COM011-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM011-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 6 18:05:46 EDT 2022
% Result : Unsatisfiable 16.51s 10.97s
% Output : Proof 16.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM011-1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 13:31:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 16.51/10.97 % SZS status Unsatisfiable
% 16.51/10.97 % SZS output start Proof
% 16.51/10.97 tff(c_lessequals_type, type, (
% 16.51/10.97 c_lessequals: ( $i * $i * $i ) > $o)).
% 16.51/10.97 tff(tc_set_type, type, (
% 16.51/10.97 tc_set: $i > $i)).
% 16.51/10.97 tff(t_a_type, type, (
% 16.51/10.97 t_a: $i)).
% 16.51/10.97 tff(v_A_type, type, (
% 16.51/10.97 v_A: $i)).
% 16.51/10.97 tff(c_minus_type, type, (
% 16.51/10.97 c_minus: ( $i * $i * $i ) > $i)).
% 16.51/10.97 tff(v_B_type, type, (
% 16.51/10.97 v_B: $i)).
% 16.51/10.97 tff(c_in_type, type, (
% 16.51/10.97 c_in: ( $i * $i * $i ) > $o)).
% 16.51/10.97 tff(c_Main_OsubsetI__1_type, type, (
% 16.51/10.97 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 16.51/10.97 tff(tc_UNITY_Oprogram_type, type, (
% 16.51/10.97 tc_UNITY_Oprogram: $i > $i)).
% 16.51/10.97 tff(c_WFair_Otransient_type, type, (
% 16.51/10.97 c_WFair_Otransient: ( $i * $i ) > $i)).
% 16.51/10.97 tff(v_F_type, type, (
% 16.51/10.97 v_F: $i)).
% 16.51/10.97 tff(c_UNITY_Oconstrains_type, type, (
% 16.51/10.97 c_UNITY_Oconstrains: ( $i * $i * $i ) > $i)).
% 16.51/10.97 tff(c_union_type, type, (
% 16.51/10.97 c_union: ( $i * $i * $i ) > $i)).
% 16.51/10.97 tff(c_WFair_Oensures_type, type, (
% 16.51/10.97 c_WFair_Oensures: ( $i * $i * $i ) > $i)).
% 16.51/10.97 tff(c_WFair_OleadsTo_type, type, (
% 16.51/10.97 c_WFair_OleadsTo: ( $i * $i * $i ) > $i)).
% 16.51/10.97 tff(1,assumption,(~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))), introduced(assumption)).
% 16.51/10.97 tff(2,plain,
% 16.51/10.97 (^[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))))),
% 16.51/10.97 inference(bind,[status(th)],[])).
% 16.51/10.97 tff(3,plain,
% 16.51/10.97 (![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)))),
% 16.51/10.97 inference(quant_intro,[status(thm)],[2])).
% 16.51/10.97 tff(4,plain,
% 16.51/10.97 (![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)))),
% 16.51/10.97 inference(rewrite,[status(thm)],[])).
% 16.51/10.97 tff(5,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/Axioms/MSC001-0.ax','cls_Set_OsubsetI_0')).
% 16.51/10.97 tff(6,plain,
% 16.51/10.97 (![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)))),
% 16.51/10.97 inference(modus_ponens,[status(thm)],[5, 4])).
% 16.51/10.97 tff(7,plain,(
% 16.51/10.97 ![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)))),
% 16.51/10.97 inference(skolemize,[status(sab)],[6])).
% 16.51/10.97 tff(8,plain,
% 16.51/10.97 (![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)))),
% 16.51/10.97 inference(modus_ponens,[status(thm)],[7, 3])).
% 16.51/10.97 tff(9,plain,
% 16.51/10.97 (((~![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_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(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_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a))),
% 16.51/10.97 inference(rewrite,[status(thm)],[])).
% 16.51/10.97 tff(10,plain,
% 16.51/10.97 ((c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a) | c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) <=> (c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a))),
% 16.51/10.97 inference(rewrite,[status(thm)],[])).
% 16.51/10.97 tff(11,plain,
% 16.51/10.97 (((~![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_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a) | c_lessequals(c_minus(v_A, v_B, tc_set(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_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)))),
% 16.51/10.98 inference(monotonicity,[status(thm)],[10])).
% 16.51/10.98 tff(12,plain,
% 16.51/10.98 (((~![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_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a) | c_lessequals(c_minus(v_A, v_B, tc_set(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_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a))),
% 16.51/10.98 inference(transitivity,[status(thm)],[11, 9])).
% 16.51/10.98 tff(13,plain,
% 16.51/10.98 ((~![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_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a) | c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)))),
% 16.51/10.98 inference(quant_inst,[status(thm)],[])).
% 16.51/10.98 tff(14,plain,
% 16.51/10.98 ((~![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_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[13, 12])).
% 16.51/10.98 tff(15,plain,
% 16.51/10.98 (c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)),
% 16.51/10.98 inference(unit_resolution,[status(thm)],[14, 8, 1])).
% 16.51/10.98 tff(16,plain,
% 16.51/10.98 (^[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))))),
% 16.51/10.98 inference(bind,[status(th)],[])).
% 16.51/10.98 tff(17,plain,
% 16.51/10.98 (![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)))),
% 16.51/10.98 inference(quant_intro,[status(thm)],[16])).
% 16.51/10.98 tff(18,plain,
% 16.51/10.98 (![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)))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(19,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/Axioms/MSC001-0.ax','cls_Set_OsubsetI_1')).
% 16.51/10.98 tff(20,plain,
% 16.51/10.98 (![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)))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[19, 18])).
% 16.51/10.98 tff(21,plain,(
% 16.51/10.98 ![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)))),
% 16.51/10.98 inference(skolemize,[status(sab)],[20])).
% 16.51/10.98 tff(22,plain,
% 16.51/10.98 (![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)))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[21, 17])).
% 16.51/10.98 tff(23,plain,
% 16.51/10.98 (((~![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_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a)) | c_lessequals(c_minus(v_A, v_B, tc_set(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_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a)) | c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(24,plain,
% 16.51/10.98 ((~![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_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a)) | c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)))),
% 16.51/10.98 inference(quant_inst,[status(thm)],[])).
% 16.51/10.98 tff(25,plain,
% 16.51/10.98 ((~![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_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a)) | c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[24, 23])).
% 16.51/10.98 tff(26,plain,
% 16.51/10.98 (~c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a)),
% 16.51/10.98 inference(unit_resolution,[status(thm)],[25, 22, 1])).
% 16.51/10.98 tff(27,plain,
% 16.51/10.98 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a)) <=> ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a)))),
% 16.51/10.98 inference(bind,[status(th)],[])).
% 16.51/10.98 tff(28,plain,
% 16.51/10.98 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))),
% 16.51/10.98 inference(quant_intro,[status(thm)],[27])).
% 16.51/10.98 tff(29,plain,
% 16.51/10.98 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(30,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))), file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax','cls_Set_ODiffE_1')).
% 16.51/10.98 tff(31,plain,
% 16.51/10.98 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[30, 29])).
% 16.51/10.98 tff(32,plain,(
% 16.51/10.98 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))),
% 16.51/10.98 inference(skolemize,[status(sab)],[31])).
% 16.51/10.98 tff(33,plain,
% 16.51/10.98 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[32, 28])).
% 16.51/10.98 tff(34,plain,
% 16.51/10.98 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))) | ((~c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))) | (~c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(35,plain,
% 16.51/10.98 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))) | ((~c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a))),
% 16.51/10.98 inference(quant_inst,[status(thm)],[])).
% 16.51/10.98 tff(36,plain,
% 16.51/10.98 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, c_minus(V_A, V_B, tc_set(T_a)), T_a)) | c_in(V_c, V_A, T_a))) | (~c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), c_minus(v_A, v_B, tc_set(t_a)), t_a)) | c_in(c_Main_OsubsetI__1(c_minus(v_A, v_B, tc_set(t_a)), v_A, t_a), v_A, t_a)),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[35, 34])).
% 16.51/10.98 tff(37,plain,
% 16.51/10.98 ($false),
% 16.51/10.98 inference(unit_resolution,[status(thm)],[36, 33, 26, 15])).
% 16.51/10.98 tff(38,plain,(c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 16.51/10.98 tff(39,assumption,(~c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))), introduced(assumption)).
% 16.51/10.98 tff(40,plain,
% 16.51/10.98 (c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) <=> c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(41,axiom,(c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 16.51/10.98 tff(42,plain,
% 16.51/10.98 (c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[41, 40])).
% 16.51/10.98 tff(43,plain,
% 16.51/10.98 (^[V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a)))) <=> ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a)))))),
% 16.51/10.98 inference(bind,[status(th)],[])).
% 16.51/10.98 tff(44,plain,
% 16.51/10.98 (![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a)))) <=> ![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(quant_intro,[status(thm)],[43])).
% 16.51/10.98 tff(45,plain,
% 16.51/10.98 (![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a)))) <=> ![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(46,plain,
% 16.51/10.98 (^[V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a))) <=> ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a)))))),
% 16.51/10.98 inference(bind,[status(th)],[])).
% 16.51/10.98 tff(47,plain,
% 16.51/10.98 (![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a))) <=> ![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(quant_intro,[status(thm)],[46])).
% 16.51/10.98 tff(48,axiom,(![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_UNITY_Oconstrains__weaken__L_0')).
% 16.51/10.98 tff(49,plain,
% 16.51/10.98 (![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[48, 47])).
% 16.51/10.98 tff(50,plain,
% 16.51/10.98 (![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[49, 45])).
% 16.51/10.98 tff(51,plain,(
% 16.51/10.98 ![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(skolemize,[status(sab)],[50])).
% 16.51/10.98 tff(52,plain,
% 16.51/10.98 (![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[51, 44])).
% 16.51/10.98 tff(53,plain,
% 16.51/10.98 (((~![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))) | ((~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))))) <=> ((~![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))) | (~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(54,plain,
% 16.51/10.98 (((~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)))) <=> ((~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(55,plain,
% 16.51/10.98 (((~![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))) | ((~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))))) <=> ((~![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))) | ((~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)))))),
% 16.51/10.98 inference(monotonicity,[status(thm)],[54])).
% 16.51/10.98 tff(56,plain,
% 16.51/10.98 (((~![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))) | ((~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))))) <=> ((~![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))) | (~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))))),
% 16.51/10.98 inference(transitivity,[status(thm)],[55, 53])).
% 16.51/10.98 tff(57,plain,
% 16.51/10.98 ((~![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))) | ((~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))))),
% 16.51/10.98 inference(quant_inst,[status(thm)],[])).
% 16.51/10.98 tff(58,plain,
% 16.51/10.98 ((~![V_F: $i, V_A_H: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_UNITY_Oconstrains(V_B, V_A_H, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_UNITY_Oconstrains(V_A, V_A_H, T_a), tc_UNITY_Oprogram(T_a))))) | (~c_in(v_F, c_UNITY_Oconstrains(v_A, c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[57, 56])).
% 16.51/10.98 tff(59,plain,
% 16.51/10.98 ($false),
% 16.51/10.98 inference(unit_resolution,[status(thm)],[58, 52, 42, 39, 38])).
% 16.51/10.98 tff(60,plain,(c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))), inference(lemma,lemma(discharge,[]))).
% 16.51/10.98 tff(61,plain,
% 16.51/10.98 ((~c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))) <=> (~c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(62,axiom,(~c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 16.51/10.98 tff(63,plain,
% 16.51/10.98 (~c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[62, 61])).
% 16.51/10.98 tff(64,plain,
% 16.51/10.98 (^[V_F: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(bind,[status(th)],[])).
% 16.51/10.98 tff(65,plain,
% 16.51/10.98 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))),
% 16.51/10.98 inference(quant_intro,[status(thm)],[64])).
% 16.51/10.98 tff(66,plain,
% 16.51/10.98 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(67,axiom,(![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_WFair_OleadsTo__Basis_0')).
% 16.51/10.98 tff(68,plain,
% 16.51/10.98 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[67, 66])).
% 16.51/10.98 tff(69,plain,(
% 16.51/10.98 ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))),
% 16.51/10.98 inference(skolemize,[status(sab)],[68])).
% 16.51/10.98 tff(70,plain,
% 16.51/10.98 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[69, 65])).
% 16.51/10.98 tff(71,plain,
% 16.51/10.98 (((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))) | ((~c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)))) <=> ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))) | (~c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(72,plain,
% 16.51/10.98 ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))) | ((~c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)))),
% 16.51/10.98 inference(quant_inst,[status(thm)],[])).
% 16.51/10.98 tff(73,plain,
% 16.51/10.98 ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) | c_in(V_F, c_WFair_OleadsTo(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))) | (~c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_OleadsTo(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[72, 71])).
% 16.51/10.98 tff(74,plain,
% 16.51/10.98 (~c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a))),
% 16.51/10.98 inference(unit_resolution,[status(thm)],[73, 70, 63])).
% 16.51/10.98 tff(75,plain,
% 16.51/10.98 (^[V_F: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a)))) <=> (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a)))))),
% 16.51/10.98 inference(bind,[status(th)],[])).
% 16.51/10.98 tff(76,plain,
% 16.51/10.98 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a)))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(quant_intro,[status(thm)],[75])).
% 16.51/10.98 tff(77,plain,
% 16.51/10.98 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a)))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(78,plain,
% 16.51/10.98 (^[V_F: $i, T_a: $i, V_B: $i, V_A: $i] : trans(monotonicity(rewrite(((~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a)))) <=> ((~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))), ((((~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a)))) | c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> (((~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a)))) | c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))))), rewrite((((~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a)))) | c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))), ((((~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a)))) | c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))))),
% 16.51/10.98 inference(bind,[status(th)],[])).
% 16.51/10.98 tff(79,plain,
% 16.51/10.98 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a)))) | c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(quant_intro,[status(thm)],[78])).
% 16.51/10.98 tff(80,axiom,(![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a)))) | c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_WFair_OensuresI_0')).
% 16.51/10.98 tff(81,plain,
% 16.51/10.98 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[80, 79])).
% 16.51/10.98 tff(82,plain,
% 16.51/10.98 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[81, 77])).
% 16.51/10.98 tff(83,plain,(
% 16.51/10.98 ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(skolemize,[status(sab)],[82])).
% 16.51/10.98 tff(84,plain,
% 16.51/10.98 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[83, 76])).
% 16.51/10.98 tff(85,plain,
% 16.51/10.98 (((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))) | (c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))))) <=> ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))) | c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(86,plain,
% 16.51/10.98 ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))) | (c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a))))),
% 16.51/10.98 inference(quant_inst,[status(thm)],[])).
% 16.51/10.98 tff(87,plain,
% 16.51/10.98 ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_F, c_WFair_Oensures(V_A, V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(c_minus(V_A, V_B, tc_set(T_a)), T_a), tc_UNITY_Oprogram(T_a))) | (~c_in(V_F, c_UNITY_Oconstrains(c_minus(V_A, V_B, tc_set(T_a)), c_union(V_A, V_B, T_a), T_a), tc_UNITY_Oprogram(T_a))))) | c_in(v_F, c_WFair_Oensures(v_A, v_B, t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[86, 85])).
% 16.51/10.98 tff(88,plain,
% 16.51/10.98 ((~c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a))) | (~c_in(v_F, c_UNITY_Oconstrains(c_minus(v_A, v_B, tc_set(t_a)), c_union(v_A, v_B, t_a), t_a), tc_UNITY_Oprogram(t_a)))),
% 16.51/10.98 inference(unit_resolution,[status(thm)],[87, 84, 74])).
% 16.51/10.98 tff(89,plain,
% 16.51/10.98 (~c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a))),
% 16.51/10.98 inference(unit_resolution,[status(thm)],[88, 60])).
% 16.51/10.98 tff(90,plain,
% 16.51/10.98 (c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a)) <=> c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(91,axiom,(c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 16.51/10.98 tff(92,plain,
% 16.51/10.98 (c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))),
% 16.51/10.98 inference(modus_ponens,[status(thm)],[91, 90])).
% 16.51/10.98 tff(93,plain,
% 16.51/10.98 (^[V_F: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a)))) <=> ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a)))))),
% 16.51/10.98 inference(bind,[status(th)],[])).
% 16.51/10.98 tff(94,plain,
% 16.51/10.98 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a)))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(quant_intro,[status(thm)],[93])).
% 16.51/10.98 tff(95,plain,
% 16.51/10.98 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a)))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(rewrite,[status(thm)],[])).
% 16.51/10.98 tff(96,plain,
% 16.51/10.98 (^[V_F: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a)))))),
% 16.51/10.98 inference(bind,[status(th)],[])).
% 16.51/10.98 tff(97,plain,
% 16.51/10.98 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a))) <=> ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.98 inference(quant_intro,[status(thm)],[96])).
% 16.51/10.98 tff(98,axiom,(![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_WFair_Otransient__strengthen_0')).
% 16.51/10.99 tff(99,plain,
% 16.51/10.99 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.99 inference(modus_ponens,[status(thm)],[98, 97])).
% 16.51/10.99 tff(100,plain,
% 16.51/10.99 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.99 inference(modus_ponens,[status(thm)],[99, 95])).
% 16.51/10.99 tff(101,plain,(
% 16.51/10.99 ![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.99 inference(skolemize,[status(sab)],[100])).
% 16.51/10.99 tff(102,plain,
% 16.51/10.99 (![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))),
% 16.51/10.99 inference(modus_ponens,[status(thm)],[101, 94])).
% 16.51/10.99 tff(103,plain,
% 16.51/10.99 (((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | ((~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))))) <=> ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))))),
% 16.51/10.99 inference(rewrite,[status(thm)],[])).
% 16.51/10.99 tff(104,plain,
% 16.51/10.99 (((~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a)))) <=> ((~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))))),
% 16.51/10.99 inference(rewrite,[status(thm)],[])).
% 16.51/10.99 tff(105,plain,
% 16.51/10.99 (((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | ((~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))))) <=> ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | ((~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)))))),
% 16.51/10.99 inference(monotonicity,[status(thm)],[104])).
% 16.51/10.99 tff(106,plain,
% 16.51/10.99 (((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | ((~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))))) <=> ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))))),
% 16.51/11.02 inference(transitivity,[status(thm)],[105, 103])).
% 16.51/11.02 tff(107,plain,
% 16.51/11.02 ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | ((~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))))),
% 16.51/11.02 inference(quant_inst,[status(thm)],[])).
% 16.51/11.02 tff(108,plain,
% 16.51/11.02 ((~![V_F: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_B, V_A, tc_set(T_a))) | c_in(V_F, c_WFair_Otransient(V_B, T_a), tc_UNITY_Oprogram(T_a)) | (~c_in(V_F, c_WFair_Otransient(V_A, T_a), tc_UNITY_Oprogram(T_a))))) | (~c_in(v_F, c_WFair_Otransient(v_A, t_a), tc_UNITY_Oprogram(t_a))) | c_in(v_F, c_WFair_Otransient(c_minus(v_A, v_B, tc_set(t_a)), t_a), tc_UNITY_Oprogram(t_a)) | (~c_lessequals(c_minus(v_A, v_B, tc_set(t_a)), v_A, tc_set(t_a)))),
% 16.51/11.02 inference(modus_ponens,[status(thm)],[107, 106])).
% 16.51/11.02 tff(109,plain,
% 16.51/11.02 ($false),
% 16.51/11.02 inference(unit_resolution,[status(thm)],[108, 102, 92, 89, 38])).
% 16.51/11.02 % SZS output end Proof
%------------------------------------------------------------------------------