TSTP Solution File: COM007+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COM007+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n012.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 : Wed Aug 30 18:35:08 EDT 2023
% Result : Theorem 3.36s 3.57s
% Output : CNFRefutation 3.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COM007+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 13:26:39 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.55 start to proof:theBenchmark
% 3.36/3.57 %-------------------------------------------
% 3.36/3.57 % File :CSE---1.6
% 3.36/3.57 % Problem :theBenchmark
% 3.36/3.57 % Transform :cnf
% 3.36/3.57 % Format :tptp:raw
% 3.36/3.57 % Command :java -jar mcs_scs.jar %d %s
% 3.36/3.57
% 3.36/3.57 % Result :Theorem 2.940000s
% 3.36/3.57 % Output :CNFRefutation 2.940000s
% 3.36/3.57 %-------------------------------------------
% 3.36/3.57 %------------------------------------------------------------------------------
% 3.36/3.57 % File : COM007+1 : TPTP v8.1.2. Released v3.2.0.
% 3.36/3.57 % Domain : Computing Theory
% 3.36/3.57 % Problem : Preservation of the Diamond Property under reflexive closure
% 3.36/3.57 % Version : Especial > Reduced > Especial.
% 3.36/3.57 % English :
% 3.36/3.57
% 3.36/3.57 % Refs : [Bez05] Bezem (2005), Email to Geoff Sutcliffe
% 3.36/3.57 % Source : [Bez05]
% 3.36/3.57 % Names : dpe [Bez05]
% 3.36/3.57
% 3.36/3.57 % Status : Theorem
% 3.36/3.57 % Rating : 0.00 v7.5.0, 0.05 v7.4.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v6.1.0, 0.12 v6.0.0, 0.25 v5.5.0, 0.12 v5.4.0, 0.13 v5.3.0, 0.17 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.05 v3.7.0, 0.33 v3.5.0, 0.12 v3.4.0, 0.08 v3.3.0, 0.00 v3.2.0
% 3.36/3.57
% 3.36/3.57 % Syntax : Number of formulae : 10 ( 2 unt; 0 def)
% 3.36/3.57 % Number of atoms : 23 ( 0 equ)
% 3.36/3.57 % Maximal formula atoms : 4 ( 2 avg)
% 3.36/3.57 % Number of connectives : 13 ( 0 ~; 1 |; 5 &)
% 3.36/3.57 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 3.36/3.57 % Maximal formula depth : 7 ( 4 avg)
% 3.36/3.57 % Maximal term depth : 1 ( 1 avg)
% 3.36/3.57 % Number of predicates : 4 ( 4 usr; 1 prp; 0-2 aty)
% 3.36/3.57 % Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% 3.36/3.57 % Number of variables : 17 ( 16 !; 1 ?)
% 3.36/3.57 % SPC : FOF_THM_RFO_NEQ
% 3.36/3.57
% 3.36/3.57 % Comments :
% 3.36/3.57 %------------------------------------------------------------------------------
% 3.36/3.57 fof(assumption,axiom,
% 3.36/3.57 ( reflexive_rewrite(a,b)
% 3.36/3.57 & reflexive_rewrite(a,c) ) ).
% 3.36/3.57
% 3.36/3.57 fof(goal_ax,axiom,
% 3.36/3.57 ! [A] :
% 3.36/3.57 ( ( reflexive_rewrite(b,A)
% 3.36/3.57 & reflexive_rewrite(c,A) )
% 3.36/3.57 => goal ) ).
% 3.36/3.57
% 3.36/3.57 fof(reflexivity,axiom,
% 3.36/3.57 ! [A] : equalish(A,A) ).
% 3.36/3.57
% 3.36/3.57 fof(symmtery,axiom,
% 3.36/3.57 ! [A,B] :
% 3.36/3.57 ( equalish(A,B)
% 3.36/3.57 => equalish(B,A) ) ).
% 3.36/3.57
% 3.36/3.57 fof(substitution,axiom,
% 3.36/3.57 ! [A,B,C] :
% 3.36/3.57 ( ( equalish(A,B)
% 3.36/3.57 & reflexive_rewrite(B,C) )
% 3.36/3.57 => reflexive_rewrite(A,C) ) ).
% 3.36/3.57
% 3.36/3.57 fof(equalish_in_reflexive_rewrite,axiom,
% 3.36/3.57 ! [A,B] :
% 3.36/3.57 ( equalish(A,B)
% 3.36/3.57 => reflexive_rewrite(A,B) ) ).
% 3.36/3.57
% 3.36/3.57 fof(rewrite_in_reflexive_rewrite,axiom,
% 3.36/3.57 ! [A,B] :
% 3.36/3.57 ( rewrite(A,B)
% 3.36/3.57 => reflexive_rewrite(A,B) ) ).
% 3.36/3.57
% 3.36/3.57 fof(equalish_or_rewrite,axiom,
% 3.36/3.57 ! [A,B] :
% 3.36/3.57 ( reflexive_rewrite(A,B)
% 3.36/3.57 => ( equalish(A,B)
% 3.36/3.57 | rewrite(A,B) ) ) ).
% 3.36/3.57
% 3.36/3.57 fof(rewrite_diamond,axiom,
% 3.36/3.57 ! [A,B,C] :
% 3.36/3.57 ( ( rewrite(A,B)
% 3.36/3.57 & rewrite(A,C) )
% 3.36/3.57 => ? [D] :
% 3.36/3.57 ( rewrite(B,D)
% 3.36/3.57 & rewrite(C,D) ) ) ).
% 3.36/3.57
% 3.36/3.57 fof(goal_to_be_proved,conjecture,
% 3.36/3.57 goal ).
% 3.36/3.57
% 3.36/3.57 %------------------------------------------------------------------------------
% 3.36/3.57 %-------------------------------------------
% 3.36/3.57 % Proof found
% 3.36/3.57 % SZS status Theorem for theBenchmark
% 3.36/3.57 % SZS output start Proof
% 3.36/3.57 %ClaNum:12(EqnAxiom:0)
% 3.36/3.57 %VarNum:44(SingletonVarNum:19)
% 3.36/3.57 %MaxLitNum:3
% 3.36/3.57 %MaxfuncDepth:1
% 3.36/3.57 %SharedTerms:8
% 3.36/3.57 %goalClause: 4
% 3.36/3.57 %singleGoalClaCount:1
% 3.36/3.57 [1]P1(a1,a2)
% 3.36/3.57 [2]P1(a1,a3)
% 3.36/3.57 [4]~P3(a500)
% 3.36/3.57 [3]P2(x31,x31)
% 3.36/3.57 [5]~P2(x51,x52)+P1(x51,x52)
% 3.36/3.57 [6]~P4(x61,x62)+P1(x61,x62)
% 3.36/3.57 [7]~P2(x72,x71)+P2(x71,x72)
% 3.36/3.57 [8]~P1(a3,x81)+~P1(a2,x81)+P3(a500)
% 3.36/3.57 [9]P4(x91,x92)+~P1(x91,x92)+P2(x91,x92)
% 3.36/3.57 [10]~P2(x101,x103)+P1(x101,x102)+~P1(x103,x102)
% 3.36/3.57 [11]~P4(x112,x113)+~P4(x112,x111)+P4(x111,f4(x112,x113,x111))
% 3.36/3.57 [12]~P4(x122,x123)+~P4(x122,x121)+P4(x121,f4(x122,x121,x123))
% 3.36/3.57 %EqnAxiom
% 3.36/3.57
% 3.36/3.57 %-------------------------------------------
% 3.36/3.58 cnf(13,plain,
% 3.36/3.58 (P1(x131,x131)),
% 3.36/3.58 inference(scs_inference,[],[3,5])).
% 3.36/3.58 cnf(14,plain,
% 3.36/3.58 (~P1(a3,a2)),
% 3.36/3.58 inference(scs_inference,[],[4,3,5,8])).
% 3.36/3.58 cnf(17,plain,
% 3.36/3.58 (~P2(a3,a1)),
% 3.36/3.58 inference(scs_inference,[],[4,3,1,5,8,6,10])).
% 3.36/3.58 cnf(19,plain,
% 3.36/3.58 (~P1(a2,x191)+~P1(a3,x191)),
% 3.36/3.58 inference(scs_inference,[],[4,8])).
% 3.36/3.58 cnf(20,plain,
% 3.36/3.58 (~P1(a2,a3)),
% 3.36/3.58 inference(scs_inference,[],[13,19])).
% 3.36/3.58 cnf(27,plain,
% 3.36/3.58 (P4(a1,a3)),
% 3.36/3.58 inference(scs_inference,[],[2,13,14,17,19,5,7,9])).
% 3.36/3.58 cnf(33,plain,
% 3.36/3.58 (P1(a3,f4(a1,a3,a3))),
% 3.36/3.58 inference(scs_inference,[],[2,13,14,17,19,5,7,9,12,11,6])).
% 3.36/3.58 cnf(47,plain,
% 3.36/3.58 (~P1(a2,f4(a1,a3,a3))),
% 3.36/3.58 inference(scs_inference,[],[33,19])).
% 3.36/3.58 cnf(56,plain,
% 3.36/3.58 (P2(a1,a2)+P4(a1,a2)),
% 3.36/3.58 inference(scs_inference,[],[47,1,5,7,9])).
% 3.36/3.58 cnf(63,plain,
% 3.36/3.58 (P2(a1,a2)+P4(a2,f4(a1,a2,a2))),
% 3.36/3.58 inference(scs_inference,[],[56,11])).
% 3.36/3.58 cnf(65,plain,
% 3.36/3.58 (~P2(a2,a1)),
% 3.36/3.58 inference(scs_inference,[],[20,2,10])).
% 3.36/3.58 cnf(67,plain,
% 3.36/3.58 (P4(a2,f4(a1,a2,a2))),
% 3.36/3.58 inference(scs_inference,[],[65,63,7])).
% 3.36/3.58 cnf(70,plain,
% 3.36/3.58 (~P2(a1,a2)),
% 3.36/3.58 inference(scs_inference,[],[67,65,12,7])).
% 3.36/3.58 cnf(72,plain,
% 3.36/3.58 (P4(a1,a2)),
% 3.36/3.58 inference(scs_inference,[],[67,65,1,12,7,9])).
% 3.36/3.58 cnf(321,plain,
% 3.36/3.58 (P4(a2,f4(a1,a3,a2))),
% 3.36/3.58 inference(scs_inference,[],[27,70,1,11,9])).
% 3.36/3.58 cnf(324,plain,
% 3.36/3.58 (P1(a2,f4(a1,a3,a2))),
% 3.36/3.58 inference(scs_inference,[],[321,11,6])).
% 3.36/3.58 cnf(331,plain,
% 3.36/3.58 ($false),
% 3.36/3.58 inference(scs_inference,[],[27,324,72,19,6,12]),
% 3.36/3.58 ['proof']).
% 3.36/3.58 % SZS output end Proof
% 3.36/3.58 % Total time :2.940000s
%------------------------------------------------------------------------------