TSTP Solution File: SWV242-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV242-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 15:10:31 EDT 2022
% Result : Unsatisfiable 14.82s 9.59s
% Output : Proof 14.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SWV242-1 : TPTP v8.1.0. Released v3.2.0.
% 0.05/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n020.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sun Sep 4 01:53:14 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.30 Usage: tptp [options] [-file:]file
% 0.10/0.30 -h, -? prints this message.
% 0.10/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.30 -m, -model generate model.
% 0.10/0.30 -p, -proof generate proof.
% 0.10/0.30 -c, -core generate unsat core of named formulas.
% 0.10/0.30 -st, -statistics display statistics.
% 0.10/0.30 -t:timeout set timeout (in second).
% 0.10/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.30 -<param>:<value> configuration parameter and value.
% 0.10/0.30 -o:<output-file> file to place output in.
% 14.82/9.59 % SZS status Unsatisfiable
% 14.82/9.59 % SZS output start Proof
% 14.82/9.59 tff(c_lessequals_type, type, (
% 14.82/9.59 c_lessequals: ( $i * $i * $i ) > $o)).
% 14.82/9.59 tff(tc_set_type, type, (
% 14.82/9.59 tc_set: $i > $i)).
% 14.82/9.59 tff(tc_Message_Omsg_type, type, (
% 14.82/9.59 tc_Message_Omsg: $i)).
% 14.82/9.59 tff(c_Message_Oanalz_type, type, (
% 14.82/9.59 c_Message_Oanalz: $i > $i)).
% 14.82/9.59 tff(c_union_type, type, (
% 14.82/9.59 c_union: ( $i * $i * $i ) > $i)).
% 14.82/9.59 tff(v_H_H_type, type, (
% 14.82/9.59 v_H_H: $i)).
% 14.82/9.59 tff(v_G_H_type, type, (
% 14.82/9.59 v_G_H: $i)).
% 14.82/9.59 tff(v_H_type, type, (
% 14.82/9.59 v_H: $i)).
% 14.82/9.59 tff(v_G_type, type, (
% 14.82/9.59 v_G: $i)).
% 14.82/9.59 tff(1,plain,
% 14.82/9.59 (^[T_a: $i, V_B: $i, V_A: $i] : refl(c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a)) <=> c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a)))),
% 14.82/9.59 inference(bind,[status(th)],[])).
% 14.82/9.59 tff(2,plain,
% 14.82/9.59 (![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a)) <=> ![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a))),
% 14.82/9.59 inference(quant_intro,[status(thm)],[1])).
% 14.82/9.59 tff(3,plain,
% 14.82/9.59 (![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a)) <=> ![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a))),
% 14.82/9.59 inference(rewrite,[status(thm)],[])).
% 14.82/9.59 tff(4,axiom,(![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUn__upper1_0')).
% 14.82/9.59 tff(5,plain,
% 14.82/9.59 (![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[4, 3])).
% 14.82/9.59 tff(6,plain,(
% 14.82/9.59 ![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a))),
% 14.82/9.59 inference(skolemize,[status(sab)],[5])).
% 14.82/9.59 tff(7,plain,
% 14.82/9.59 (![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[6, 2])).
% 14.82/9.59 tff(8,plain,
% 14.82/9.59 ((~![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a))) | c_lessequals(v_G_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 14.82/9.59 inference(quant_inst,[status(thm)],[])).
% 14.82/9.59 tff(9,plain,
% 14.82/9.59 (c_lessequals(v_G_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 14.82/9.59 inference(unit_resolution,[status(thm)],[8, 7])).
% 14.82/9.59 tff(10,assumption,(~c_lessequals(c_Message_Oanalz(v_G_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 14.82/9.59 tff(11,plain,
% 14.82/9.59 (^[V_H: $i, V_G: $i] : refl(((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg))) <=> ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg))))),
% 14.82/9.59 inference(bind,[status(th)],[])).
% 14.82/9.59 tff(12,plain,
% 14.82/9.59 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(quant_intro,[status(thm)],[11])).
% 14.82/9.59 tff(13,plain,
% 14.82/9.59 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(rewrite,[status(thm)],[])).
% 14.82/9.59 tff(14,axiom,(![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oanalz__mono_0')).
% 14.82/9.59 tff(15,plain,
% 14.82/9.59 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[14, 13])).
% 14.82/9.59 tff(16,plain,(
% 14.82/9.59 ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(skolemize,[status(sab)],[15])).
% 14.82/9.59 tff(17,plain,
% 14.82/9.59 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[16, 12])).
% 14.82/9.59 tff(18,plain,
% 14.82/9.59 (((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(v_G_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(v_G_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(v_G_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(v_G_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(rewrite,[status(thm)],[])).
% 14.82/9.59 tff(19,plain,
% 14.82/9.59 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(v_G_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(v_G_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(quant_inst,[status(thm)],[])).
% 14.82/9.59 tff(20,plain,
% 14.82/9.59 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(v_G_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(v_G_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[19, 18])).
% 14.82/9.59 tff(21,plain,
% 14.82/9.59 ($false),
% 14.82/9.59 inference(unit_resolution,[status(thm)],[20, 17, 10, 9])).
% 14.82/9.59 tff(22,plain,(c_lessequals(c_Message_Oanalz(v_G_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 14.82/9.59 tff(23,assumption,(~c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 14.82/9.59 tff(24,plain,
% 14.82/9.59 (c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)) <=> c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg))),
% 14.82/9.59 inference(rewrite,[status(thm)],[])).
% 14.82/9.59 tff(25,axiom,(c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 14.82/9.59 tff(26,plain,
% 14.82/9.59 (c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[25, 24])).
% 14.82/9.59 tff(27,plain,
% 14.82/9.59 (^[T_a: $i, V_B: $i, V_A: $i, V_C: $i] : refl((c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) <=> (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))))),
% 14.82/9.59 inference(bind,[status(th)],[])).
% 14.82/9.59 tff(28,plain,
% 14.82/9.59 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 14.82/9.59 inference(quant_intro,[status(thm)],[27])).
% 14.82/9.59 tff(29,plain,
% 14.82/9.59 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 14.82/9.59 inference(rewrite,[status(thm)],[])).
% 14.82/9.59 tff(30,plain,
% 14.82/9.59 (^[T_a: $i, V_B: $i, V_A: $i, V_C: $i] : trans(monotonicity(rewrite(((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) <=> ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))), ((((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(V_A, V_C, tc_set(T_a))) <=> (((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) | c_lessequals(V_A, V_C, tc_set(T_a))))), rewrite((((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) | c_lessequals(V_A, V_C, tc_set(T_a))) <=> (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))), ((((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(V_A, V_C, tc_set(T_a))) <=> (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))))),
% 14.82/9.59 inference(bind,[status(th)],[])).
% 14.82/9.59 tff(31,plain,
% 14.82/9.59 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(V_A, V_C, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 14.82/9.59 inference(quant_intro,[status(thm)],[30])).
% 14.82/9.59 tff(32,axiom,(![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(V_A, V_C, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_Osubset__trans_0')).
% 14.82/9.59 tff(33,plain,
% 14.82/9.59 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[32, 31])).
% 14.82/9.59 tff(34,plain,
% 14.82/9.59 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[33, 29])).
% 14.82/9.59 tff(35,plain,(
% 14.82/9.59 ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 14.82/9.59 inference(skolemize,[status(sab)],[34])).
% 14.82/9.59 tff(36,plain,
% 14.82/9.59 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[35, 28])).
% 14.82/9.59 tff(37,plain,
% 14.82/9.59 (((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_G_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_G_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))),
% 14.82/9.59 inference(rewrite,[status(thm)],[])).
% 14.82/9.59 tff(38,plain,
% 14.82/9.59 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_G_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))),
% 14.82/9.59 inference(quant_inst,[status(thm)],[])).
% 14.82/9.59 tff(39,plain,
% 14.82/9.59 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_G_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[38, 37])).
% 14.82/9.59 tff(40,plain,
% 14.82/9.59 ($false),
% 14.82/9.59 inference(unit_resolution,[status(thm)],[39, 36, 26, 23, 22])).
% 14.82/9.59 tff(41,plain,(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 14.82/9.59 tff(42,plain,
% 14.82/9.59 (((~c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))),
% 14.82/9.59 inference(rewrite,[status(thm)],[])).
% 14.82/9.59 tff(43,axiom,((~c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 14.82/9.59 tff(44,plain,
% 14.82/9.59 ((~c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[43, 42])).
% 14.82/9.59 tff(45,plain,
% 14.82/9.59 ((~c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[44, 42])).
% 14.82/9.59 tff(46,plain,
% 14.82/9.59 ((~c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[45, 42])).
% 14.82/9.59 tff(47,plain,
% 14.82/9.59 ((~c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[46, 42])).
% 14.82/9.59 tff(48,plain,
% 14.82/9.59 ((~c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[47, 42])).
% 14.82/9.59 tff(49,plain,
% 14.82/9.59 ((~c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[48, 42])).
% 14.82/9.59 tff(50,plain,
% 14.82/9.59 ((~c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[49, 42])).
% 14.82/9.59 tff(51,plain,
% 14.82/9.59 ((~c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.82/9.59 inference(modus_ponens,[status(thm)],[50, 42])).
% 14.82/9.59 tff(52,plain,
% 14.82/9.59 (~c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 14.90/9.59 inference(unit_resolution,[status(thm)],[51, 41])).
% 14.90/9.59 tff(53,plain,
% 14.90/9.59 (c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg)) <=> c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg))),
% 14.90/9.59 inference(rewrite,[status(thm)],[])).
% 14.90/9.59 tff(54,axiom,(c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 14.90/9.59 tff(55,plain,
% 14.90/9.59 (c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg))),
% 14.90/9.59 inference(modus_ponens,[status(thm)],[54, 53])).
% 14.90/9.59 tff(56,plain,
% 14.90/9.59 (((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_H_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_H_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))),
% 14.90/9.59 inference(rewrite,[status(thm)],[])).
% 14.90/9.59 tff(57,plain,
% 14.90/9.59 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_H_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))),
% 14.90/9.59 inference(quant_inst,[status(thm)],[])).
% 14.90/9.59 tff(58,plain,
% 14.90/9.59 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(V_A, V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_H_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.90/9.59 inference(modus_ponens,[status(thm)],[57, 56])).
% 14.90/9.59 tff(59,plain,
% 14.90/9.59 (~c_lessequals(c_Message_Oanalz(v_H_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 14.90/9.59 inference(unit_resolution,[status(thm)],[58, 36, 55, 52])).
% 14.90/9.59 tff(60,plain,
% 14.90/9.59 (^[T_a: $i, V_B: $i, V_A: $i] : refl(c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a)) <=> c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a)))),
% 14.90/9.59 inference(bind,[status(th)],[])).
% 14.90/9.59 tff(61,plain,
% 14.90/9.59 (![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a)) <=> ![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a))),
% 14.90/9.59 inference(quant_intro,[status(thm)],[60])).
% 14.90/9.59 tff(62,plain,
% 14.90/9.59 (![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a)) <=> ![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a))),
% 14.90/9.59 inference(rewrite,[status(thm)],[])).
% 14.90/9.59 tff(63,axiom,(![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUn__upper2_0')).
% 14.90/9.59 tff(64,plain,
% 14.90/9.59 (![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a))),
% 14.90/9.59 inference(modus_ponens,[status(thm)],[63, 62])).
% 14.90/9.59 tff(65,plain,(
% 14.90/9.59 ![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a))),
% 14.90/9.59 inference(skolemize,[status(sab)],[64])).
% 14.90/9.62 tff(66,plain,
% 14.90/9.62 (![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a))),
% 14.90/9.62 inference(modus_ponens,[status(thm)],[65, 61])).
% 14.90/9.62 tff(67,plain,
% 14.90/9.62 ((~![T_a: $i, V_B: $i, V_A: $i] : c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a))) | c_lessequals(v_H_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 14.90/9.62 inference(quant_inst,[status(thm)],[])).
% 14.90/9.62 tff(68,plain,
% 14.90/9.62 (c_lessequals(v_H_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 14.90/9.62 inference(unit_resolution,[status(thm)],[67, 66])).
% 14.90/9.62 tff(69,plain,
% 14.90/9.62 (((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(v_H_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(v_H_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(v_H_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(v_H_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.90/9.62 inference(rewrite,[status(thm)],[])).
% 14.90/9.62 tff(70,plain,
% 14.90/9.62 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(v_H_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(v_H_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 14.90/9.62 inference(quant_inst,[status(thm)],[])).
% 14.90/9.62 tff(71,plain,
% 14.90/9.62 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(v_H_H, c_union(v_G_H, v_H_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(v_H_H), c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 14.90/9.62 inference(modus_ponens,[status(thm)],[70, 69])).
% 14.90/9.62 tff(72,plain,
% 14.90/9.62 ($false),
% 14.90/9.62 inference(unit_resolution,[status(thm)],[71, 17, 68, 59])).
% 14.90/9.62 % SZS output end Proof
%------------------------------------------------------------------------------