TSTP Solution File: LCL893+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL893+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n025.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 Aug 31 06:51:30 EDT 2023
% Result : Theorem 0.19s 0.74s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL893+1 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 19:27:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.63 start to proof:theBenchmark
% 0.19/0.73 %-------------------------------------------
% 0.19/0.73 % File :CSE---1.6
% 0.19/0.73 % Problem :theBenchmark
% 0.19/0.73 % Transform :cnf
% 0.19/0.73 % Format :tptp:raw
% 0.19/0.73 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.73
% 0.19/0.73 % Result :Theorem 0.070000s
% 0.19/0.73 % Output :CNFRefutation 0.070000s
% 0.19/0.73 %-------------------------------------------
% 0.19/0.73 %--------------------------------------------------------------------------
% 0.19/0.73 % File : LCL893+1 : TPTP v8.1.2. Released v5.5.0.
% 0.19/0.74 % Domain : Logic Calculi (Continuous Propositional)
% 0.19/0.74 % Problem : In a coop, x/2 = x implies x = 0
% 0.19/0.74 % Version : [AO13] axioms : Especial.
% 0.19/0.74 % English :
% 0.19/0.74
% 0.19/0.74 % Refs : [Art12] Arthan (2012), Email to Geoff Sutcliffe
% 0.19/0.74 % : [AO13] Arthan & Olica (2013), Dual Hoops Have Unique Halving
% 0.19/0.74 % Source : [Art12]
% 0.19/0.74 % Names : pr2.tptp [Art12]
% 0.19/0.74
% 0.19/0.74 % Status : Theorem
% 0.19/0.74 % Rating : 0.25 v8.1.0, 0.19 v7.4.0, 0.20 v7.3.0, 0.17 v7.1.0, 0.22 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.25 v6.2.0, 0.28 v6.1.0, 0.27 v6.0.0, 0.26 v5.5.0
% 0.19/0.74 % Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% 0.19/0.74 % Number of atoms : 24 ( 9 equ)
% 0.19/0.74 % Maximal formula atoms : 3 ( 1 avg)
% 0.19/0.74 % Number of connectives : 9 ( 0 ~; 0 |; 2 &)
% 0.19/0.74 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 0.19/0.74 % Maximal formula depth : 6 ( 4 avg)
% 0.19/0.74 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.74 % Number of predicates : 2 ( 1 usr; 0 prp; 2-2 aty)
% 0.19/0.74 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 0.19/0.74 % Number of variables : 30 ( 30 !; 0 ?)
% 0.19/0.74 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.74
% 0.19/0.74 % Comments :
% 0.19/0.74 %--------------------------------------------------------------------------
% 0.19/0.74 fof(sos_01,axiom,
% 0.19/0.74 ! [A,B,C] : '+'('+'(A,B),C) = '+'(A,'+'(B,C)) ).
% 0.19/0.74
% 0.19/0.74 fof(sos_02,axiom,
% 0.19/0.74 ! [A,B] : '+'(A,B) = '+'(B,A) ).
% 0.19/0.74
% 0.19/0.74 fof(sos_03,axiom,
% 0.19/0.74 ! [A] : '+'(A,'0') = A ).
% 0.19/0.74
% 0.19/0.74 fof(sos_04,axiom,
% 0.19/0.74 ! [A] : '+'(A,'1') = '1' ).
% 0.19/0.74
% 0.19/0.74 fof(sos_05,axiom,
% 0.19/0.74 ! [A] : '>='(A,A) ).
% 0.19/0.74
% 0.19/0.74 fof(sos_06,axiom,
% 0.19/0.74 ! [X0,X1,X2] :
% 0.19/0.74 ( ( '>='(X0,X1)
% 0.19/0.74 & '>='(X1,X2) )
% 0.19/0.74 => '>='(X0,X2) ) ).
% 0.19/0.74
% 0.19/0.74 fof(sos_07,axiom,
% 0.19/0.74 ! [X3,X4] :
% 0.19/0.74 ( ( '>='(X3,X4)
% 0.19/0.74 & '>='(X4,X3) )
% 0.19/0.74 => X3 = X4 ) ).
% 0.19/0.74
% 0.19/0.74 fof(sos_08,axiom,
% 0.19/0.74 ! [X5,X6,X7] :
% 0.19/0.74 ( '>='('+'(X5,X6),X7)
% 0.19/0.74 <=> '>='(X6,'==>'(X5,X7)) ) ).
% 0.19/0.74
% 0.19/0.74 fof(sos_09,axiom,
% 0.19/0.74 ! [A] : '>='(A,'0') ).
% 0.19/0.74
% 0.19/0.74 fof(sos_10,axiom,
% 0.19/0.74 ! [X8,X9,X10] :
% 0.19/0.74 ( '>='(X8,X9)
% 0.19/0.74 => '>='('+'(X8,X10),'+'(X9,X10)) ) ).
% 0.19/0.74
% 0.19/0.74 fof(sos_11,axiom,
% 0.19/0.74 ! [X11,X12,X13] :
% 0.19/0.74 ( '>='(X11,X12)
% 0.19/0.74 => '>='('==>'(X12,X13),'==>'(X11,X13)) ) ).
% 0.19/0.74
% 0.19/0.74 fof(sos_12,axiom,
% 0.19/0.74 ! [X14,X15,X16] :
% 0.19/0.74 ( '>='(X14,X15)
% 0.19/0.74 => '>='('==>'(X16,X14),'==>'(X16,X15)) ) ).
% 0.19/0.74
% 0.19/0.74 fof(sos_13,axiom,
% 0.19/0.74 ! [A,B] : '+'(A,'==>'(A,B)) = '+'(B,'==>'(B,A)) ).
% 0.19/0.74
% 0.19/0.74 fof(sos_14,axiom,
% 0.19/0.74 ! [A] : h(A) = '==>'(h(A),A) ).
% 0.19/0.74
% 0.19/0.74 fof(goals_15,conjecture,
% 0.19/0.74 ! [X17] :
% 0.19/0.74 ( h(X17) = X17
% 0.19/0.74 => X17 = '0' ) ).
% 0.19/0.74
% 0.19/0.74 %--------------------------------------------------------------------------
% 0.19/0.74 %-------------------------------------------
% 0.19/0.74 % Proof found
% 0.19/0.74 % SZS status Theorem for theBenchmark
% 0.19/0.74 % SZS output start Proof
% 0.19/0.74 %ClaNum:27(EqnAxiom:10)
% 0.19/0.74 %VarNum:67(SingletonVarNum:32)
% 0.19/0.74 %MaxLitNum:3
% 0.19/0.74 %MaxfuncDepth:2
% 0.19/0.74 %SharedTerms:6
% 0.19/0.74 %goalClause: 11 20
% 0.19/0.74 %singleGoalClaCount:2
% 0.19/0.74 [20]~E(a4,a1)
% 0.19/0.74 [11]E(f6(a1),a1)
% 0.19/0.74 [13]P1(x131,a4)
% 0.19/0.74 [15]P1(x151,x151)
% 0.19/0.74 [12]E(f3(x121,a2),a2)
% 0.19/0.74 [14]E(f3(x141,a4),x141)
% 0.19/0.74 [16]E(f5(f6(x161),x161),f6(x161))
% 0.19/0.74 [17]E(f3(x171,x172),f3(x172,x171))
% 0.19/0.74 [18]E(f3(x181,f5(x181,x182)),f3(x182,f5(x182,x181)))
% 0.19/0.74 [19]E(f3(f3(x191,x192),x193),f3(x191,f3(x192,x193)))
% 0.19/0.74 [23]~P1(x231,x233)+P1(f3(x231,x232),f3(x233,x232))
% 0.19/0.74 [24]~P1(x242,x243)+P1(f5(x241,x242),f5(x241,x243))
% 0.19/0.74 [25]~P1(x253,x251)+P1(f5(x251,x252),f5(x253,x252))
% 0.19/0.74 [26]~P1(f3(x262,x261),x263)+P1(x261,f5(x262,x263))
% 0.19/0.74 [27]~P1(x272,f5(x271,x273))+P1(f3(x271,x272),x273)
% 0.19/0.74 [21]~P1(x212,x211)+~P1(x211,x212)+E(x211,x212)
% 0.19/0.74 [22]~P1(x221,x223)+P1(x221,x222)+~P1(x223,x222)
% 0.19/0.74 %EqnAxiom
% 0.19/0.74 [1]E(x11,x11)
% 0.19/0.74 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.74 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.74 [4]~E(x41,x42)+E(f6(x41),f6(x42))
% 0.19/0.74 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53))
% 0.19/0.74 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62))
% 0.19/0.74 [7]~E(x71,x72)+E(f5(x71,x73),f5(x72,x73))
% 0.19/0.74 [8]~E(x81,x82)+E(f5(x83,x81),f5(x83,x82))
% 0.19/0.74 [9]P1(x92,x93)+~E(x91,x92)+~P1(x91,x93)
% 0.19/0.74 [10]P1(x103,x102)+~E(x101,x102)+~P1(x103,x101)
% 0.19/0.74
% 0.19/0.74 %-------------------------------------------
% 0.19/0.74 cnf(28,plain,
% 0.19/0.74 (E(a1,f6(a1))),
% 0.19/0.74 inference(scs_inference,[],[11,2])).
% 0.19/0.74 cnf(29,plain,
% 0.19/0.74 (P1(f6(a1),a1)),
% 0.19/0.74 inference(scs_inference,[],[11,15,2,10])).
% 0.19/0.74 cnf(30,plain,
% 0.19/0.74 (P1(x301,x301)),
% 0.19/0.74 inference(rename_variables,[],[15])).
% 0.19/0.74 cnf(31,plain,
% 0.19/0.74 (P1(a1,f6(a1))),
% 0.19/0.74 inference(scs_inference,[],[11,15,30,2,10,9])).
% 0.19/0.74 cnf(32,plain,
% 0.19/0.74 (P1(x321,x321)),
% 0.19/0.74 inference(rename_variables,[],[15])).
% 0.19/0.74 cnf(33,plain,
% 0.19/0.74 (~E(a4,f6(a1))),
% 0.19/0.74 inference(scs_inference,[],[11,15,30,20,2,10,9,3])).
% 0.19/0.74 cnf(38,plain,
% 0.19/0.74 (E(f6(f6(a1)),f6(a1))),
% 0.19/0.74 inference(scs_inference,[],[11,15,30,20,2,10,9,3,8,7,6,5,4])).
% 0.19/0.74 cnf(39,plain,
% 0.19/0.74 (P1(f5(a4,x391),f5(x392,x391))),
% 0.19/0.74 inference(scs_inference,[],[11,15,30,13,20,2,10,9,3,8,7,6,5,4,25])).
% 0.19/0.74 cnf(45,plain,
% 0.19/0.74 (P1(f3(x451,f5(x451,x452)),x452)),
% 0.19/0.74 inference(scs_inference,[],[11,15,30,32,13,20,2,10,9,3,8,7,6,5,4,25,24,23,27])).
% 0.19/0.74 cnf(46,plain,
% 0.19/0.74 (P1(x461,x461)),
% 0.19/0.74 inference(rename_variables,[],[15])).
% 0.19/0.74 cnf(48,plain,
% 0.19/0.74 (P1(x481,f5(x482,f3(x482,x481)))),
% 0.19/0.74 inference(scs_inference,[],[11,15,30,32,46,13,20,2,10,9,3,8,7,6,5,4,25,24,23,27,26])).
% 0.19/0.74 cnf(51,plain,
% 0.19/0.74 (~P1(a4,a1)),
% 0.19/0.74 inference(scs_inference,[],[11,15,30,32,46,13,20,2,10,9,3,8,7,6,5,4,25,24,23,27,26,21])).
% 0.19/0.74 cnf(54,plain,
% 0.19/0.74 (~E(a1,a4)),
% 0.19/0.74 inference(scs_inference,[],[20,2])).
% 0.19/0.74 cnf(56,plain,
% 0.19/0.74 (~E(a4,f3(f6(a1),a4))),
% 0.19/0.74 inference(scs_inference,[],[11,14,20,51,33,2,10,3])).
% 0.19/0.74 cnf(57,plain,
% 0.19/0.74 (E(f3(x571,a4),x571)),
% 0.19/0.74 inference(rename_variables,[],[14])).
% 0.19/0.74 cnf(59,plain,
% 0.19/0.74 (P1(x591,f5(x592,f3(x592,x591)))),
% 0.19/0.74 inference(rename_variables,[],[48])).
% 0.19/0.74 cnf(62,plain,
% 0.19/0.74 (~P1(f3(a4,a4),a1)),
% 0.19/0.74 inference(scs_inference,[],[11,14,57,20,13,48,51,33,2,10,3,21,9])).
% 0.19/0.74 cnf(64,plain,
% 0.19/0.74 (~P1(f5(x641,f3(x641,a4)),a1)),
% 0.19/0.74 inference(scs_inference,[],[11,14,57,20,13,48,59,51,33,2,10,3,21,9,22])).
% 0.19/0.74 cnf(67,plain,
% 0.19/0.74 (~P1(a4,f5(a4,a1))),
% 0.19/0.74 inference(scs_inference,[],[11,14,57,20,13,48,59,51,33,2,10,3,21,9,22,27])).
% 0.19/0.74 cnf(75,plain,
% 0.19/0.74 (E(a2,f3(x751,a2))),
% 0.19/0.74 inference(scs_inference,[],[12,13,39,48,27,21,2])).
% 0.19/0.74 cnf(77,plain,
% 0.19/0.74 (P1(x771,x771)),
% 0.19/0.74 inference(rename_variables,[],[15])).
% 0.19/0.74 cnf(82,plain,
% 0.19/0.74 (~P1(f3(a4,a4),f3(x821,f5(x821,a1)))),
% 0.19/0.74 inference(scs_inference,[],[12,16,15,77,13,45,39,62,38,48,27,21,2,10,3,9,22])).
% 0.19/0.74 cnf(90,plain,
% 0.19/0.74 (~E(f3(a4,a4),f3(x901,f5(x901,a1)))),
% 0.19/0.74 inference(scs_inference,[],[15,13,82,56,27,21,10])).
% 0.19/0.74 cnf(91,plain,
% 0.19/0.74 (P1(x911,x911)),
% 0.19/0.74 inference(rename_variables,[],[15])).
% 0.19/0.74 cnf(93,plain,
% 0.19/0.74 (~E(f3(x931,f5(x931,a1)),f3(a4,a4))),
% 0.19/0.74 inference(scs_inference,[],[15,91,13,82,56,27,21,10,2,9])).
% 0.19/0.74 cnf(95,plain,
% 0.19/0.74 (~E(a4,f3(a4,f6(a1)))),
% 0.19/0.74 inference(scs_inference,[],[17,15,91,13,82,56,27,21,10,2,9,3])).
% 0.19/0.74 cnf(99,plain,
% 0.19/0.74 (~P1(a4,f3(f5(a4,a1),a4))),
% 0.19/0.74 inference(scs_inference,[],[12,14,67,6,10])).
% 0.19/0.74 cnf(100,plain,
% 0.19/0.74 (E(f3(x1001,a4),x1001)),
% 0.19/0.74 inference(rename_variables,[],[14])).
% 0.19/0.74 cnf(102,plain,
% 0.19/0.74 (~E(a4,f3(x1021,f5(x1021,a1)))),
% 0.19/0.74 inference(scs_inference,[],[12,19,14,100,90,67,6,10,2,3])).
% 0.19/0.74 cnf(103,plain,
% 0.19/0.74 (E(f3(x1031,a4),x1031)),
% 0.19/0.74 inference(rename_variables,[],[14])).
% 0.19/0.74 cnf(104,plain,
% 0.19/0.74 (~P1(f3(a4,a4),f5(a4,a1))),
% 0.19/0.74 inference(scs_inference,[],[12,19,14,100,103,90,67,6,10,2,3,9])).
% 0.19/0.74 cnf(106,plain,
% 0.19/0.74 (P1(f5(x1061,f6(a1)),f5(x1061,a1))),
% 0.19/0.74 inference(scs_inference,[],[12,29,19,14,100,103,90,67,6,10,2,3,9,24])).
% 0.19/0.74 cnf(109,plain,
% 0.19/0.74 (P1(f5(a1,x1091),f5(f6(a1),x1091))),
% 0.19/0.74 inference(scs_inference,[],[12,29,19,14,100,103,90,67,6,10,2,3,9,24,7,25])).
% 0.19/0.74 cnf(113,plain,
% 0.19/0.74 (P1(x1131,f5(x1132,a4))),
% 0.19/0.74 inference(scs_inference,[],[12,29,19,14,100,103,13,90,67,6,10,2,3,9,24,7,25,23,26])).
% 0.19/0.74 cnf(126,plain,
% 0.19/0.74 (~P1(f3(a4,f3(a4,a4)),a1)),
% 0.19/0.74 inference(scs_inference,[],[104,26])).
% 0.19/0.74 cnf(132,plain,
% 0.19/0.74 (P1(f3(x1321,f5(x1321,x1322)),f3(x1322,f5(x1322,x1321)))),
% 0.19/0.74 inference(scs_inference,[],[18,15,104,93,26,27,6,10])).
% 0.19/0.74 cnf(133,plain,
% 0.19/0.74 (P1(x1331,x1331)),
% 0.19/0.74 inference(rename_variables,[],[15])).
% 0.19/0.74 cnf(135,plain,
% 0.19/0.74 (~E(f3(x1351,f5(x1351,a1)),a4)),
% 0.19/0.74 inference(scs_inference,[],[12,18,15,104,93,102,75,26,27,6,10,3,2])).
% 0.19/0.74 cnf(136,plain,
% 0.19/0.74 (P1(f3(x1361,x1362),f3(x1362,x1361))),
% 0.19/0.74 inference(scs_inference,[],[12,18,17,15,133,104,93,102,75,26,27,6,10,3,2,9])).
% 0.19/0.74 cnf(138,plain,
% 0.19/0.74 (E(f5(x1381,a1),f5(x1381,f6(a1)))+~P1(f5(x1381,a1),f5(x1381,f6(a1)))),
% 0.19/0.74 inference(scs_inference,[],[12,18,17,15,133,104,93,106,102,75,26,27,6,10,3,2,9,21])).
% 0.19/0.74 cnf(143,plain,
% 0.19/0.74 (P1(x1431,f5(x1432,f3(x1432,a4)))),
% 0.19/0.74 inference(scs_inference,[],[13,132,48,26,22])).
% 0.19/0.74 cnf(148,plain,
% 0.19/0.74 (~P1(a4,f3(x1481,f5(x1481,a1)))),
% 0.19/0.74 inference(scs_inference,[],[13,132,109,135,48,26,22,27,21])).
% 0.19/0.74 cnf(154,plain,
% 0.19/0.74 (E(f6(x1541),f5(f6(x1541),x1541))),
% 0.19/0.74 inference(scs_inference,[],[13,28,16,15,132,109,64,135,48,26,22,27,21,6,10,2])).
% 0.19/0.74 cnf(155,plain,
% 0.19/0.74 (~E(a4,f5(f6(a1),a1))),
% 0.19/0.74 inference(scs_inference,[],[13,28,16,15,132,109,64,135,33,48,26,22,27,21,6,10,2,3])).
% 0.19/0.74 cnf(159,plain,
% 0.19/0.74 (~P1(f3(f3(a4,a4),a4),a1)),
% 0.19/0.74 inference(scs_inference,[],[136,126,22])).
% 0.19/0.74 cnf(173,plain,
% 0.19/0.74 (~P1(f3(a4,a4),f3(f5(a4,a1),a4))),
% 0.19/0.74 inference(scs_inference,[],[13,28,18,14,136,113,54,148,126,99,95,22,27,21,10,2,3,9])).
% 0.19/0.74 cnf(175,plain,
% 0.19/0.74 (~P1(f3(f3(a4,a4),a4),f6(a1))),
% 0.19/0.74 inference(scs_inference,[],[29,159,22])).
% 0.19/0.74 cnf(180,plain,
% 0.19/0.74 (P1(f3(x1801,a4),x1801)),
% 0.19/0.74 inference(scs_inference,[],[14,29,15,143,159,22,27,6,10])).
% 0.19/0.74 cnf(181,plain,
% 0.19/0.74 (P1(x1811,x1811)),
% 0.19/0.74 inference(rename_variables,[],[15])).
% 0.19/0.74 cnf(186,plain,
% 0.19/0.74 (P1(x1861,f3(x1861,a4))),
% 0.19/0.74 inference(scs_inference,[],[14,19,17,29,15,181,143,159,22,27,6,10,3,2,9])).
% 0.19/0.74 cnf(188,plain,
% 0.19/0.74 (P1(f5(x1881,a1),f5(x1881,f6(a1)))),
% 0.19/0.74 inference(scs_inference,[],[14,31,19,17,29,15,181,143,159,22,27,6,10,3,2,9,24])).
% 0.19/0.74 cnf(217,plain,
% 0.19/0.74 (~P1(f3(f6(a1),a4),a1)),
% 0.19/0.74 inference(scs_inference,[],[18,31,154,173,186,188,175,155,90,13,138,22,27,21,10,2,3,9,26])).
% 0.19/0.74 cnf(221,plain,
% 0.19/0.74 ($false),
% 0.19/0.74 inference(scs_inference,[],[29,180,217,26,22]),
% 0.19/0.74 ['proof']).
% 0.19/0.74 % SZS output end Proof
% 0.19/0.74 % Total time :0.070000s
%------------------------------------------------------------------------------