%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL031-1 : TPTP v8.2.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n029.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 04:44:51 EDT 2024 % Result : Unsatisfiable 58.57s 59.15s % Output : CNFRefutation 58.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : COL031-1 : TPTP v8.2.0. Released v1.0.0. % 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n029.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Jun 18 16:05:54 EDT 2024 % 0.12/0.35 % CPUTime : % 0.42/0.59 start to proof:theBenchmark % 58.57/59.13 %------------------------------------------- % 58.57/59.13 % File :CSE---1.7 % 58.57/59.13 % Problem :theBenchmark % 58.57/59.13 % Transform :cnf % 58.57/59.13 % Format :tptp:raw % 58.57/59.13 % Command :java -jar mcs_scs.jar %d %s % 58.57/59.13 % 58.57/59.13 % Result :Theorem 58.000000s % 58.57/59.13 % Output :CNFRefutation 58.000000s % 58.57/59.13 %------------------------------------------- % 58.57/59.14 %-------------------------------------------------------------------------- % 58.57/59.14 % File : COL031-1 : TPTP v8.2.0. Released v1.0.0. % 58.57/59.14 % Domain : Combinatory Logic % 58.57/59.14 % Problem : Strong fixed point for L and O % 58.57/59.14 % Version : [WM88] (equality) axioms. % 58.57/59.14 % English : The strong fixed point property holds for the set % 58.57/59.14 % P consisting of the combinators L and O, where (Lx)y = x(yy), % 58.57/59.14 % (Ox)y = y(xy). % 58.57/59.14 % 58.57/59.14 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi % 58.57/59.14 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem % 58.57/59.14 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq % 58.57/59.14 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb % 58.57/59.14 % Source : [MW88] % 58.57/59.14 % Names : - [MW88] % 58.57/59.14 % 58.57/59.14 % Status : Unsatisfiable % 58.57/59.14 % Rating : 0.09 v8.2.0, 0.12 v8.1.0, 0.20 v7.5.0, 0.17 v7.4.0, 0.26 v7.3.0, 0.21 v7.1.0, 0.11 v7.0.0, 0.05 v6.4.0, 0.11 v6.3.0, 0.12 v6.2.0, 0.07 v6.1.0, 0.00 v6.0.0, 0.10 v5.5.0, 0.05 v5.4.0, 0.00 v5.1.0, 0.07 v5.0.0, 0.00 v2.0.0 % 58.57/59.14 % Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR) % 58.57/59.14 % Number of literals : 3 ( 3 equ; 1 neg) % 58.57/59.14 % Maximal clause size : 1 ( 1 avg) % 58.57/59.14 % Maximal term depth : 4 ( 2 avg) % 58.57/59.14 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 58.57/59.15 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty) % 58.57/59.15 % Number of variables : 5 ( 0 sgn) % 58.57/59.15 % SPC : CNF_UNS_RFO_PEQ_UEQ % 58.57/59.15 % 58.57/59.15 % Comments : % 58.57/59.15 %-------------------------------------------------------------------------- % 58.57/59.15 cnf(l_definition,axiom, % 58.57/59.15 apply(apply(l,X),Y) = apply(X,apply(Y,Y)) ). % 58.57/59.15 % 58.57/59.15 cnf(o_definition,axiom, % 58.57/59.15 apply(apply(o,X),Y) = apply(Y,apply(X,Y)) ). % 58.57/59.15 % 58.57/59.15 cnf(prove_fixed_point,negated_conjecture, % 58.57/59.15 apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ). % 58.57/59.15 % 58.57/59.15 %-------------------------------------------------------------------------- % 58.57/59.15 %------------------------------------------- % 58.57/59.15 % Proof found % 58.57/59.15 % SZS status Theorem for theBenchmark % 58.57/59.15 % SZS output start Proof % 58.57/59.16 %ClaNum:9(EqnAxiom:6) % 58.57/59.16 %VarNum:15(SingletonVarNum:5) % 58.57/59.16 %MaxLitNum:1 % 58.57/59.16 %MaxfuncDepth:3 % 58.57/59.16 %SharedTerms:2 % 58.57/59.16 %goalClause: 9 % 58.57/59.16 %singleGoalClaCount:1 % 58.57/59.16 [9]~E(f2(f3(x91),f2(x91,f3(x91))),f2(x91,f3(x91))) % 58.57/59.16 [7]E(f2(f2(a1,x71),x72),f2(x71,f2(x72,x72))) % 58.57/59.16 [8]E(f2(f2(a4,x81),x82),f2(x82,f2(x81,x82))) % 58.57/59.16 %EqnAxiom % 58.57/59.16 [1]E(x11,x11) % 58.57/59.16 [2]E(x22,x21)+~E(x21,x22) % 58.57/59.16 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 58.57/59.16 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 58.57/59.16 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 58.57/59.16 [6]~E(x61,x62)+E(f3(x61),f3(x62)) % 58.57/59.16 % 58.57/59.16 %------------------------------------------- % 58.62/59.17 cnf(10,plain, % 58.62/59.17 (E(f2(x101,f2(x102,x102)),f2(f2(a1,x101),x102))), % 58.62/59.17 inference(scs_inference,[],[7,2])). % 58.62/59.17 cnf(11,plain, % 58.62/59.17 (E(f2(x111,f2(x112,x111)),f2(f2(a4,x112),x111))), % 58.62/59.17 inference(scs_inference,[],[8,2])). % 58.62/59.17 cnf(20,plain, % 58.62/59.17 (~E(f2(f2(a4,x201),f3(x201)),f2(x201,f3(x201)))), % 58.62/59.17 inference(scs_inference,[],[7,11,9,6,4,5,2,3])). % 58.62/59.17 cnf(25,plain, % 58.62/59.17 ($false), % 58.62/59.17 inference(scs_inference,[],[20,10,6,5,4]), % 58.62/59.17 ['proof']). % 58.62/59.17 % SZS output end Proof % 58.62/59.17 % Total time :58.000000s %------------------------------------------------------------------------------