%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET047-5 : TPTP v8.2.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n032.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 : Mon Jun 24 14:20:18 EDT 2024 % Result : Unsatisfiable 0.13s 0.49s % Output : CNFRefutation 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.08 % Problem : SET047-5 : TPTP v8.2.0. Released v1.0.0. % 0.00/0.08 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.06/0.26 % Computer : n032.cluster.edu % 0.06/0.26 % Model : x86_64 x86_64 % 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.26 % Memory : 8042.1875MB % 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.26 % CPULimit : 300 % 0.06/0.26 % WCLimit : 300 % 0.06/0.26 % DateTime : Sun Jun 23 12:34:23 EDT 2024 % 0.06/0.27 % CPUTime : % 0.13/0.44 start to proof:theBenchmark % 0.13/0.49 %------------------------------------------- % 0.13/0.49 % File :CSE---1.7 % 0.13/0.49 % Problem :theBenchmark % 0.13/0.49 % Transform :cnf % 0.13/0.49 % Format :tptp:raw % 0.13/0.49 % Command :java -jar mcs_scs.jar %d %s % 0.13/0.49 % 0.13/0.49 % Result :Theorem 0.010000s % 0.13/0.49 % Output :CNFRefutation 0.010000s % 0.13/0.49 %------------------------------------------- % 0.13/0.49 %-------------------------------------------------------------------------- % 0.13/0.49 % File : SET047-5 : TPTP v8.2.0. Released v1.0.0. % 0.13/0.49 % Domain : Set Theory % 0.13/0.49 % Problem : Set equality is symmetric % 0.13/0.49 % Version : [Pel86] axioms : Incomplete. % 0.13/0.49 % English : Define set equality as having exactly the same members. Prove % 0.13/0.49 % set equality is symmetric. % 0.13/0.49 % 0.13/0.49 % Refs : [DeC79] DeChampeaux (1979), Sub-problem Finder and Instance Ch % 0.13/0.49 % : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au % 0.13/0.49 % Source : [Pel86] % 0.13/0.49 % Names : Pelletier 43 [Pel86] % 0.13/0.49 % : p43.in [ANL] % 0.13/0.49 % 0.13/0.49 % Status : Unsatisfiable % 0.13/0.49 % Rating : 0.00 v6.3.0, 0.14 v6.2.0, 0.00 v5.1.0, 0.09 v5.0.0, 0.07 v4.1.0, 0.12 v4.0.1, 0.00 v2.1.0, 0.00 v2.0.0 % 0.13/0.49 % Syntax : Number of clauses : 6 ( 0 unt; 2 nHn; 5 RR) % 0.13/0.49 % Number of literals : 16 ( 0 equ; 8 neg) % 0.13/0.49 % Maximal clause size : 3 ( 2 avg) % 0.13/0.49 % Maximal term depth : 2 ( 1 avg) % 0.13/0.49 % Number of predicates : 2 ( 2 usr; 0 prp; 2-2 aty) % 0.13/0.49 % Number of functors : 3 ( 3 usr; 2 con; 0-2 aty) % 0.13/0.49 % Number of variables : 10 ( 0 sgn) % 0.13/0.49 % SPC : CNF_UNS_RFO_NEQ_NHN % 0.13/0.49 % 0.13/0.49 % Comments : % 0.13/0.49 %-------------------------------------------------------------------------- % 0.13/0.49 cnf(element_substitution1,axiom, % 0.13/0.49 ( ~ set_equal(X,Y) % 0.13/0.49 | ~ element(Z,X) % 0.13/0.49 | element(Z,Y) ) ). % 0.13/0.49 % 0.13/0.49 cnf(element_substitution2,axiom, % 0.13/0.49 ( ~ set_equal(X,Y) % 0.13/0.49 | ~ element(Z,Y) % 0.13/0.49 | element(Z,X) ) ). % 0.13/0.49 % 0.13/0.49 cnf(clause_3,axiom, % 0.13/0.49 ( element(f(X,Y),X) % 0.13/0.49 | element(f(X,Y),Y) % 0.13/0.49 | set_equal(X,Y) ) ). % 0.13/0.49 % 0.13/0.49 cnf(clause_4,axiom, % 0.13/0.49 ( ~ element(f(X,Y),Y) % 0.13/0.49 | ~ element(f(X,Y),X) % 0.13/0.49 | set_equal(X,Y) ) ). % 0.13/0.49 % 0.13/0.49 cnf(prove_symmetry1,negated_conjecture, % 0.13/0.49 ( set_equal(a,b) % 0.13/0.49 | set_equal(b,a) ) ). % 0.13/0.49 % 0.13/0.49 cnf(prove_symmetry2,negated_conjecture, % 0.13/0.49 ( ~ set_equal(b,a) % 0.13/0.49 | ~ set_equal(a,b) ) ). % 0.13/0.49 % 0.13/0.49 %-------------------------------------------------------------------------- % 0.13/0.49 %------------------------------------------- % 0.13/0.49 % Proof found % 0.13/0.49 % SZS status Theorem for theBenchmark % 0.13/0.49 % SZS output start Proof % 0.13/0.49 %ClaNum:6(EqnAxiom:0) % 0.13/0.49 %VarNum:28(SingletonVarNum:10) % 0.13/0.49 %MaxLitNum:3 % 0.13/0.49 %MaxfuncDepth:1 % 0.13/0.49 %SharedTerms:6 % 0.13/0.49 %goalClause: 1 2 % 0.13/0.49 [1]P1(a1,a2)+P1(a2,a1) % 0.13/0.49 [2]~P1(a1,a2)+~P1(a2,a1) % 0.13/0.49 [5]P1(x51,x52)+P2(f3(x51,x52),x52)+P2(f3(x51,x52),x51) % 0.13/0.49 [6]P1(x61,x62)+~P2(f3(x61,x62),x62)+~P2(f3(x61,x62),x61) % 0.13/0.49 [3]~P2(x31,x33)+P2(x31,x32)+~P1(x33,x32) % 0.13/0.49 [4]~P2(x41,x43)+P2(x41,x42)+~P1(x42,x43) % 0.13/0.49 %EqnAxiom % 0.13/0.49 % 0.13/0.49 %------------------------------------------- % 0.13/0.50 cnf(8,plain, % 0.13/0.50 (~P2(x81,a1)+P2(x81,a2)+P1(a2,a1)), % 0.13/0.50 inference(scs_inference,[],[3,1])). % 0.13/0.50 cnf(9,plain, % 0.13/0.50 (~P2(x91,a2)+P2(x91,a1)+P1(a2,a1)), % 0.13/0.50 inference(scs_inference,[],[4,1])). % 0.13/0.50 cnf(12,plain, % 0.13/0.50 (~P2(f3(a1,a2),a2)+~P2(f3(a1,a2),a1)+~P1(a2,a1)), % 0.13/0.50 inference(scs_inference,[],[6,2])). % 0.13/0.50 cnf(15,plain, % 0.13/0.50 (~P2(x151,a2)+P2(x151,a1)+P1(a1,a2)), % 0.13/0.50 inference(scs_inference,[],[1,3])). % 0.13/0.50 cnf(16,plain, % 0.13/0.50 (~P2(f3(a1,a2),a2)+P1(a1,a2)+~P1(a2,a1)), % 0.13/0.50 inference(scs_inference,[],[15,12])). % 0.13/0.50 cnf(17,plain, % 0.13/0.50 (P1(a1,a2)+P2(f3(a1,a2),a1)+~P1(a2,a1)), % 0.13/0.50 inference(scs_inference,[],[16,5])). % 0.13/0.50 cnf(18,plain, % 0.13/0.50 (P2(f3(a1,a2),a1)+~P1(a2,a1)), % 0.13/0.50 inference(scs_inference,[],[17,2])). % 0.13/0.50 cnf(19,plain, % 0.13/0.50 (~P1(x191,a1)+P2(f3(a1,a2),x191)+~P1(a2,a1)), % 0.13/0.50 inference(scs_inference,[],[18,4])). % 0.13/0.50 cnf(20,plain, % 0.13/0.50 (~P2(f3(a1,a2),a1)+~P1(a2,a1)), % 0.13/0.50 inference(scs_inference,[],[19,12])). % 0.13/0.50 cnf(21,plain, % 0.13/0.50 (~P1(a2,a1)), % 0.13/0.50 inference(scs_inference,[],[20,18])). % 0.13/0.50 cnf(23,plain, % 0.13/0.50 (P2(x231,a2)+~P2(x231,a1)), % 0.13/0.50 inference(scs_inference,[],[21,8])). % 0.13/0.50 cnf(24,plain, % 0.13/0.50 (P2(x241,a1)+~P2(x241,a2)), % 0.13/0.50 inference(scs_inference,[],[21,9])). % 0.13/0.50 cnf(28,plain, % 0.13/0.50 (~P2(f3(a2,a1),a1)), % 0.13/0.50 inference(scs_inference,[],[21,23,6])). % 0.13/0.50 cnf(31,plain, % 0.13/0.50 ($false), % 0.13/0.50 inference(scs_inference,[],[21,28,5,24]), % 0.13/0.50 ['proof']). % 0.13/0.50 % SZS output end Proof % 0.13/0.50 % Total time :0.010000s %------------------------------------------------------------------------------