TSTP Solution File: ROB016-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : ROB016-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 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 Aug 31 14:07:10 EDT 2023
% Result : Unsatisfiable 0.21s 0.64s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ROB016-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 06:52:14 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.57 start to proof:theBenchmark
% 0.21/0.64 %-------------------------------------------
% 0.21/0.64 % File :CSE---1.6
% 0.21/0.64 % Problem :theBenchmark
% 0.21/0.64 % Transform :cnf
% 0.21/0.64 % Format :tptp:raw
% 0.21/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.64
% 0.21/0.64 % Result :Theorem 0.010000s
% 0.21/0.64 % Output :CNFRefutation 0.010000s
% 0.21/0.64 %-------------------------------------------
% 0.21/0.64 %--------------------------------------------------------------------------
% 0.21/0.64 % File : ROB016-1 : TPTP v8.1.2. Released v1.0.0.
% 0.21/0.64 % Domain : Robbins Algebra
% 0.21/0.64 % Problem : If -(d + e) = -e then -(e + k(d + -(d + -e))) = -e, for k>0
% 0.21/0.64 % Version : [Win90] (equality) axioms.
% 0.21/0.64 % English :
% 0.21/0.64
% 0.21/0.64 % Refs : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
% 0.21/0.64 % Source : [Win90]
% 0.21/0.64 % Names : Corollary 3.7 [Win90]
% 0.21/0.64
% 0.21/0.64 % Status : Unsatisfiable
% 0.21/0.64 % Rating : 0.00 v7.0.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.00 v6.0.0, 0.11 v5.5.0, 0.50 v5.4.0, 0.47 v5.3.0, 0.67 v5.2.0, 0.12 v5.1.0, 0.14 v5.0.0, 0.29 v4.1.0, 0.11 v4.0.1, 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0, 0.29 v2.5.0, 0.00 v2.4.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.14 v2.1.0, 0.20 v2.0.0
% 0.21/0.64 % Syntax : Number of clauses : 11 ( 8 unt; 0 nHn; 6 RR)
% 0.21/0.64 % Number of literals : 15 ( 9 equ; 5 neg)
% 0.21/0.64 % Maximal clause size : 3 ( 1 avg)
% 0.21/0.64 % Maximal term depth : 8 ( 2 avg)
% 0.21/0.64 % Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% 0.21/0.64 % Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% 0.21/0.64 % Number of variables : 14 ( 0 sgn)
% 0.21/0.64 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.21/0.64
% 0.21/0.64 % Comments : The extra lemma is required for the proof.
% 0.21/0.64 %--------------------------------------------------------------------------
% 0.21/0.64 %----Include axioms for Robbins algebra
% 0.21/0.64 include('Axioms/ROB001-0.ax').
% 0.21/0.64 %----Include axioms for Robbins algebra numbers
% 0.21/0.64 include('Axioms/ROB001-1.ax').
% 0.21/0.64 %--------------------------------------------------------------------------
% 0.21/0.64 cnf(condition,hypothesis,
% 0.21/0.64 negate(add(d,e)) = negate(e) ).
% 0.21/0.64
% 0.21/0.64 cnf(k_positive,axiom,
% 0.21/0.64 positive_integer(k) ).
% 0.21/0.64
% 0.21/0.64 %----Lemma 3.6 required
% 0.21/0.64 cnf(lemma_3_6,axiom,
% 0.21/0.64 ( negate(add(negate(Y),negate(add(X,negate(Y))))) != X
% 0.21/0.64 | ~ positive_integer(Vk)
% 0.21/0.64 | negate(add(Y,multiply(Vk,add(X,negate(add(X,negate(Y))))))) = negate(Y) ) ).
% 0.21/0.64
% 0.21/0.64 cnf(prove_result,negated_conjecture,
% 0.21/0.64 negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e) ).
% 0.21/0.64
% 0.21/0.64 %--------------------------------------------------------------------------
% 0.21/0.64 %-------------------------------------------
% 0.21/0.64 % Proof found
% 0.21/0.64 % SZS status Theorem for theBenchmark
% 0.21/0.64 % SZS output start Proof
% 0.21/0.64 %ClaNum:21(EqnAxiom:10)
% 0.21/0.64 %VarNum:36(SingletonVarNum:14)
% 0.21/0.64 %MaxLitNum:3
% 0.21/0.64 %MaxfuncDepth:7
% 0.21/0.64 %SharedTerms:16
% 0.21/0.64 %goalClause: 18
% 0.21/0.64 %singleGoalClaCount:1
% 0.21/0.64 [11]P1(a1)
% 0.21/0.64 [12]P1(a2)
% 0.21/0.64 [14]E(f7(f4(a3,a5)),f7(a5))
% 0.21/0.64 [18]~E(f7(f4(a5,f6(a2,f4(a3,f7(f4(a3,f7(a5))))))),f7(a5))
% 0.21/0.64 [13]E(f6(a1,x131),x131)
% 0.21/0.64 [15]E(f4(x151,x152),f4(x152,x151))
% 0.21/0.64 [17]E(f7(f4(f7(f4(x171,x172)),f7(f4(x171,f7(x172))))),x171)
% 0.21/0.64 [16]E(f4(f4(x161,x162),x163),f4(x161,f4(x162,x163)))
% 0.21/0.64 [19]~P1(x191)+P1(f8(x191))
% 0.21/0.64 [20]~P1(x201)+E(f4(x201,f6(x202,x201)),f6(f8(x202),x201))
% 0.21/0.64 [21]~P1(x212)+~E(f7(f4(f7(x211),f7(f4(x213,f7(x211))))),x213)+E(f7(f4(x211,f6(x212,f4(x213,f7(f4(x213,f7(x211))))))),f7(x211))
% 0.21/0.64 %EqnAxiom
% 0.21/0.64 [1]E(x11,x11)
% 0.21/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.64 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.21/0.64 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.21/0.64 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 0.21/0.64 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 0.21/0.64 [8]~E(x81,x82)+E(f7(x81),f7(x82))
% 0.21/0.64 [9]~E(x91,x92)+E(f8(x91),f8(x92))
% 0.21/0.65 [10]~P1(x101)+P1(x102)+~E(x101,x102)
% 0.21/0.65
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 cnf(22,plain,
% 0.21/0.65 (E(f7(a5),f7(f4(a3,a5)))),
% 0.21/0.65 inference(scs_inference,[],[14,2])).
% 0.21/0.65 cnf(23,plain,
% 0.21/0.65 (~E(f4(a5,f6(a2,f4(a3,f7(f4(a3,f7(a5)))))),a5)),
% 0.21/0.65 inference(scs_inference,[],[18,14,2,8])).
% 0.21/0.65 cnf(25,plain,
% 0.21/0.65 (~E(f7(f4(f7(a5),f7(f4(a3,f7(a5))))),a3)),
% 0.21/0.65 inference(scs_inference,[],[18,12,14,2,8,3,21])).
% 0.21/0.65 cnf(36,plain,
% 0.21/0.65 (~E(a1,x361)+P1(x361)),
% 0.21/0.65 inference(scs_inference,[],[18,11,12,14,2,8,3,21,19,9,7,6,5,4,20,10])).
% 0.21/0.65 cnf(52,plain,
% 0.21/0.65 (~E(f7(f4(f7(a5),f7(f4(a3,f7(a5))))),f7(f4(f7(f4(a3,x521)),f7(f4(a3,f7(x521))))))),
% 0.21/0.65 inference(scs_inference,[],[17,25,8,2,3])).
% 0.21/0.65 cnf(66,plain,
% 0.21/0.65 ($false),
% 0.21/0.65 inference(scs_inference,[],[12,23,22,15,13,52,8,2,3,36,20,19,9,7,5,6]),
% 0.21/0.65 ['proof']).
% 0.21/0.65 % SZS output end Proof
% 0.21/0.65 % Total time :0.010000s
%------------------------------------------------------------------------------