TSTP Solution File: SWV239-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV239-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 : Thu Sep 29 15:10:30 EDT 2022
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV239-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 02:10:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(c_lessequals_type, type, (
% 0.13/0.40 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(tc_set_type, type, (
% 0.13/0.40 tc_set: $i > $i)).
% 0.13/0.40 tff(tc_Message_Omsg_type, type, (
% 0.13/0.40 tc_Message_Omsg: $i)).
% 0.13/0.40 tff(c_Message_Oanalz_type, type, (
% 0.13/0.40 c_Message_Oanalz: $i > $i)).
% 0.13/0.40 tff(v_H_type, type, (
% 0.13/0.40 v_H: $i)).
% 0.13/0.40 tff(v_G_type, type, (
% 0.13/0.40 v_G: $i)).
% 0.13/0.40 tff(c_in_type, type, (
% 0.13/0.40 c_in: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(c_Main_OsubsetI__1_type, type, (
% 0.13/0.40 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 0.13/0.40 tff(c_union_type, type, (
% 0.13/0.40 c_union: ( $i * $i * $i ) > $i)).
% 0.13/0.40 tff(1,assumption,(~c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (^[T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 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_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OsubsetI_1')).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.40 tff(7,plain,(
% 0.13/0.40 ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg)) | c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg)))) <=> ((~![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_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg)) | c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg)) | c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg)) | c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (^[T_a: $i, V_B: $i, V_A: $i] : refl((c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(16,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/sandbox/benchmark/theBenchmark.p','cls_Set_OsubsetI_0')).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.40 tff(18,plain,(
% 0.13/0.40 ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[17])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg))) <=> ((~![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_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 ((c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg) | c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg))) <=> (c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg) | c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg)))) <=> ((~![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_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[21])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg) | c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg)))) <=> ((~![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_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg))),
% 0.13/0.40 inference(transitivity,[status(thm)],[22, 20])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg) | c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[25, 19, 1])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(30,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_Oanalz__analzD__dest_0')).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.40 tff(32,plain,(
% 0.13/0.40 ![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.13/0.40 inference(skolemize,[status(sab)],[31])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg))) <=> ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[36, 33, 26, 12])).
% 0.13/0.40 tff(38,plain,(c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (^[V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : refl((c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg)))) <=> (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg)))) <=> ![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg)))) <=> ![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (^[V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : trans(monotonicity(rewrite(((~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg)))) <=> ((~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))), ((((~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg)))) | c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> (((~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg)))) | c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))), rewrite((((~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg)))) | c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))), ((((~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg)))) | c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (((~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg)))) | c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> ![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.13/0.41 tff(44,axiom,(![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (((~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg)))) | c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_Oanalz__subset__cong_0')).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 (![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.13/0.41 tff(47,plain,(
% 0.13/0.41 ![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[46])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 ((~c_lessequals(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> (~c_lessequals(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(50,axiom,(~c_lessequals(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (~c_lessequals(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (((~![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))) | (c_lessequals(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))))) <=> ((~![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))) | c_lessequals(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 ((~![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))) | (c_lessequals(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 ((~![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))) | c_lessequals(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 ((~c_lessequals(c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(v_G), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[54, 51, 48])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[55, 38])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (^[T_a: $i, V_A: $i] : refl(c_lessequals(V_A, V_A, tc_set(T_a)) <=> c_lessequals(V_A, V_A, tc_set(T_a)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a)) <=> ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[57])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a)) <=> ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(60,axiom,(![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_Osubset__refl_0')).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.13/0.41 tff(62,plain,(
% 0.13/0.41 ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.13/0.41 inference(skolemize,[status(sab)],[61])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 ((~![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))) | c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[64, 63, 56])).
% 0.13/0.41 % SZS output end Proof
%------------------------------------------------------------------------------