%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL039-1 : 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 : n004.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 04:44:52 EDT 2024 % Result : Unsatisfiable 116.66s 116.74s % Output : CNFRefutation 116.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : COL039-1 : TPTP v8.2.0. Released v1.0.0. % 0.04/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.11/0.33 % Computer : n004.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Tue Jun 18 16:09:38 EDT 2024 % 0.11/0.33 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 116.66/116.71 %------------------------------------------- % 116.66/116.71 % File :CSE---1.7 % 116.66/116.71 % Problem :theBenchmark % 116.66/116.71 % Transform :cnf % 116.66/116.71 % Format :tptp:raw % 116.66/116.71 % Command :java -jar mcs_scs.jar %d %s % 116.66/116.71 % 116.66/116.71 % Result :Theorem 116.080000s % 116.66/116.71 % Output :CNFRefutation 116.080000s % 116.66/116.71 %------------------------------------------- % 116.66/116.74 %-------------------------------------------------------------------------- % 116.66/116.74 % File : COL039-1 : TPTP v8.2.0. Released v1.0.0. % 116.66/116.74 % Domain : Combinatory Logic % 116.66/116.74 % Problem : Strong fixed point for B, O, and M % 116.66/116.74 % Version : [WM88] (equality) axioms. % 116.66/116.74 % English : The strong fixed point property holds for the set % 116.66/116.74 % P consisting of the combinators B, O, and M, where ((Bx)y)z % 116.66/116.74 % = x(yz), Mx = xx, (Ox)y = y(xy). % 116.66/116.74 % 116.66/116.74 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi % 116.66/116.74 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem % 116.66/116.74 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq % 116.66/116.74 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb % 116.66/116.74 % Source : [MW88] % 116.66/116.74 % Names : - [MW88] % 116.66/116.74 % 116.66/116.74 % Status : Unsatisfiable % 116.66/116.74 % Rating : 0.14 v8.2.0, 0.21 v8.1.0, 0.25 v7.4.0, 0.35 v7.3.0, 0.26 v7.1.0, 0.17 v7.0.0, 0.16 v6.4.0, 0.21 v6.3.0, 0.18 v6.2.0, 0.14 v6.1.0, 0.19 v6.0.0, 0.24 v5.5.0, 0.21 v5.4.0, 0.20 v5.3.0, 0.25 v5.2.0, 0.21 v5.1.0, 0.13 v5.0.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.08 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v3.1.0, 0.22 v2.7.0, 0.09 v2.6.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.00 v2.1.0, 0.25 v2.0.0 % 116.66/116.74 % Syntax : Number of clauses : 4 ( 4 unt; 0 nHn; 1 RR) % 116.66/116.74 % Number of literals : 4 ( 4 equ; 1 neg) % 116.66/116.74 % Maximal clause size : 1 ( 1 avg) % 116.66/116.74 % Maximal term depth : 4 ( 2 avg) % 116.66/116.74 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 116.66/116.74 % Number of functors : 5 ( 5 usr; 3 con; 0-2 aty) % 116.66/116.74 % Number of variables : 7 ( 0 sgn) % 116.66/116.74 % SPC : CNF_UNS_RFO_PEQ_UEQ % 116.66/116.74 % 116.66/116.74 % Comments : % 116.66/116.74 %-------------------------------------------------------------------------- % 116.66/116.74 cnf(b_definition,axiom, % 116.66/116.74 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ). % 116.66/116.74 % 116.66/116.74 cnf(m_definition,axiom, % 116.66/116.74 apply(m,X) = apply(X,X) ). % 116.66/116.74 % 116.66/116.74 cnf(o_definition,axiom, % 116.66/116.74 apply(apply(o,X),Y) = apply(Y,apply(X,Y)) ). % 116.66/116.74 % 116.66/116.74 cnf(prove_fixed_point,negated_conjecture, % 116.66/116.74 apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ). % 116.66/116.74 % 116.66/116.74 %-------------------------------------------------------------------------- % 116.66/116.74 %------------------------------------------- % 116.66/116.74 % Proof found % 116.66/116.74 % SZS status Theorem for theBenchmark % 116.66/116.74 % SZS output start Proof % 116.66/116.76 %ClaNum:10(EqnAxiom:6) % 116.66/116.76 %VarNum:19(SingletonVarNum:7) % 116.66/116.76 %MaxLitNum:1 % 116.66/116.76 %MaxfuncDepth:3 % 116.66/116.76 %SharedTerms:3 % 116.66/116.76 %goalClause: 10 % 116.66/116.76 %singleGoalClaCount:1 % 116.66/116.76 [7]E(f2(a1,x71),f2(x71,x71)) % 116.66/116.76 [10]~E(f2(f4(x101),f2(x101,f4(x101))),f2(x101,f4(x101))) % 116.66/116.76 [8]E(f2(f2(a5,x81),x82),f2(x82,f2(x81,x82))) % 116.66/116.76 [9]E(f2(f2(f2(a3,x91),x92),x93),f2(x91,f2(x92,x93))) % 116.66/116.76 %EqnAxiom % 116.66/116.76 [1]E(x11,x11) % 116.66/116.76 [2]E(x22,x21)+~E(x21,x22) % 116.66/116.76 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 116.66/116.76 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 116.66/116.76 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 116.66/116.76 [6]~E(x61,x62)+E(f4(x61),f4(x62)) % 116.66/116.76 % 116.66/116.76 %------------------------------------------- % 116.74/116.78 cnf(11,plain, % 116.74/116.78 (E(f2(x111,x111),f2(a1,x111))), % 116.74/116.78 inference(scs_inference,[],[7,2])). % 116.74/116.78 cnf(12,plain, % 116.74/116.78 (E(f2(a1,f2(a5,x121)),f2(f2(a5,x121),f2(x121,f2(a5,x121))))), % 116.74/116.78 inference(scs_inference,[],[7,8,2,3])). % 116.74/116.78 cnf(16,plain, % 116.74/116.78 (~E(f2(f4(a1),f2(a1,f4(a1))),f2(f4(a1),f4(a1)))), % 116.74/116.78 inference(scs_inference,[],[10,11,12,2,3])). % 116.74/116.78 cnf(19,plain, % 116.74/116.78 (~E(f2(a1,f4(a1)),f4(a1))), % 116.74/116.78 inference(scs_inference,[],[10,11,12,2,3,5])). % 116.74/116.78 cnf(20,plain, % 116.74/116.78 (E(f2(x201,f2(x202,x203)),f2(f2(f2(a3,x201),x202),x203))), % 116.74/116.78 inference(scs_inference,[],[9,2])). % 116.74/116.78 cnf(21,plain, % 116.74/116.78 (E(f2(x211,f2(x212,x211)),f2(f2(a5,x212),x211))), % 116.74/116.78 inference(scs_inference,[],[8,2])). % 116.74/116.78 cnf(22,plain, % 116.74/116.78 (E(f2(f2(a5,a5),a1),f2(f2(a5,a1),f2(a1,f2(a5,a1))))), % 116.74/116.78 inference(scs_inference,[],[8,12,3])). % 116.74/116.78 cnf(25,plain, % 116.74/116.78 (E(f2(f2(a5,a1),f2(a1,f2(a5,a1))),f2(f2(a5,a5),a1))), % 116.74/116.78 inference(scs_inference,[],[8,12,3,2])). % 116.74/116.78 cnf(26,plain, % 116.74/116.78 (E(f2(f2(a5,a1),f2(a5,a1)),f2(f2(a5,a5),a1))), % 116.74/116.78 inference(scs_inference,[],[8,25,3])). % 116.74/116.78 cnf(28,plain, % 116.74/116.78 (E(f2(f2(a5,a5),a1),f2(f2(a5,a1),f2(a5,a1)))), % 116.74/116.78 inference(scs_inference,[],[8,25,3,2])). % 116.74/116.78 cnf(48,plain, % 116.74/116.78 (E(f4(f2(a1,x481)),f4(f2(x481,x481)))), % 116.74/116.78 inference(scs_inference,[],[7,6])). % 116.74/116.78 cnf(49,plain, % 116.74/116.78 (E(f2(f2(a1,x491),x492),f2(f2(x491,x491),x492))), % 116.74/116.78 inference(scs_inference,[],[7,6,4])). % 116.74/116.78 cnf(50,plain, % 116.74/116.78 (E(f2(x501,f2(a1,x502)),f2(x501,f2(x502,x502)))), % 116.74/116.78 inference(scs_inference,[],[7,6,4,5])). % 116.74/116.78 cnf(52,plain, % 116.74/116.78 (~E(f2(f4(a1),f4(a1)),f4(a1))), % 116.74/116.78 inference(scs_inference,[],[7,19,6,4,5,2,3])). % 116.74/116.78 cnf(56,plain, % 116.74/116.78 (E(f2(x561,f2(f2(a5,a1),f2(a5,a1))),f2(x561,f2(f2(a5,a5),a1)))), % 116.74/116.78 inference(scs_inference,[],[26,6,4,5])). % 116.74/116.78 cnf(58,plain, % 116.74/116.78 (~E(f2(f2(a5,a1),f4(a1)),f2(f4(a1),f4(a1)))), % 116.74/116.78 inference(scs_inference,[],[52,26,21,16,6,4,5,2,3])). % 116.74/116.78 cnf(63,plain, % 116.74/116.78 (~E(f2(f4(a1),f4(a1)),f2(f2(a5,a1),f4(a1)))), % 116.74/116.78 inference(scs_inference,[],[49,58,6,4,5,2])). % 116.74/116.78 cnf(64,plain, % 116.74/116.78 (~E(f2(f4(a1),f2(f4(a1),f4(a1))),f2(f4(a1),f4(a1)))), % 116.74/116.78 inference(scs_inference,[],[49,50,58,16,6,4,5,2,3])). % 116.74/116.78 cnf(70,plain, % 116.74/116.78 (~E(f2(f2(f2(a3,f4(a1)),f4(a1)),f4(a1)),f2(f4(a1),f4(a1)))), % 116.74/116.78 inference(scs_inference,[],[48,64,20,6,4,5,2,3])). % 116.74/116.78 cnf(74,plain, % 116.74/116.78 (E(f2(x741,f2(f2(a5,a5),a1)),f2(x741,f2(f2(a5,a1),f2(a5,a1))))), % 116.74/116.78 inference(scs_inference,[],[28,6,4,5])). % 116.74/116.78 cnf(75,plain, % 116.74/116.78 (~E(f2(f4(a1),f4(a1)),f2(f2(f2(a3,f4(a1)),f4(a1)),f4(a1)))), % 116.74/116.78 inference(scs_inference,[],[70,28,6,4,5,2])). % 116.74/116.78 cnf(76,plain, % 116.74/116.78 (~E(f2(a1,f4(a1)),f2(f2(a5,a1),f4(a1)))), % 116.74/116.78 inference(scs_inference,[],[63,70,28,11,6,4,5,2,3])). % 116.74/116.78 cnf(80,plain, % 116.74/116.78 (E(f2(x801,f2(x802,f2(x803,x802))),f2(x801,f2(f2(a5,x803),x802)))), % 116.74/116.78 inference(scs_inference,[],[21,6,4,5])). % 116.74/116.78 cnf(82,plain, % 116.74/116.78 (~E(f2(f2(a5,x821),f4(x821)),f2(x821,f4(x821)))), % 116.74/116.78 inference(scs_inference,[],[76,21,10,6,4,5,2,3])). % 116.74/116.78 cnf(88,plain, % 116.74/116.78 (~E(f2(a1,f4(a1)),f2(f2(f2(a3,f4(a1)),f4(a1)),f4(a1)))), % 116.74/116.78 inference(scs_inference,[],[82,75,50,11,6,4,5,2,3])). % 116.74/116.78 cnf(90,plain, % 116.74/116.78 (E(f4(f2(x901,x901)),f4(f2(a1,x901)))), % 116.74/116.78 inference(scs_inference,[],[11,6])). % 116.74/116.78 cnf(91,plain, % 116.74/116.78 (E(f2(f2(x911,x911),x912),f2(f2(a1,x911),x912))), % 116.74/116.78 inference(scs_inference,[],[11,6,4])). % 116.74/116.78 cnf(92,plain, % 116.74/116.78 (E(f2(x921,f2(x922,x922)),f2(x921,f2(a1,x922)))), % 116.74/116.78 inference(scs_inference,[],[11,6,4,5])). % 116.74/116.78 cnf(93,plain, % 116.74/116.78 (~E(f2(f2(f2(a3,f4(a1)),f4(a1)),f4(a1)),f2(a1,f4(a1)))), % 116.74/116.78 inference(scs_inference,[],[88,11,6,4,5,2])). % 116.74/116.78 cnf(94,plain, % 116.74/116.78 (E(f2(f2(a5,a5),a1),f2(f2(a5,a1),f2(f2(a5,a5),a1)))), % 116.74/116.78 inference(scs_inference,[],[88,22,80,11,6,4,5,2,3])). % 116.74/116.78 cnf(98,plain, % 116.74/116.78 (E(f2(x981,f2(f2(x982,x982),x983)),f2(x981,f2(f2(a1,x982),x983)))), % 116.74/116.78 inference(scs_inference,[],[91,6,4,5])). % 116.74/116.78 cnf(100,plain, % 116.74/116.78 (~E(f2(f4(a1),f2(f4(a1),f4(a1))),f2(a1,f4(a1)))), % 116.74/116.78 inference(scs_inference,[],[91,93,16,9,6,4,5,2,3])). % 116.74/116.78 cnf(106,plain, % 116.74/116.78 (E(f2(f2(a5,a5),a1),f2(f2(a5,a1),f2(f2(a5,a1),f2(a5,a1))))), % 116.74/116.78 inference(scs_inference,[],[92,100,94,74,6,4,5,2,3])). % 116.74/116.78 cnf(112,plain, % 116.74/116.78 (~E(f2(f2(f2(a3,f4(a1)),a1),f4(a1)),f2(f4(a1),f4(a1)))), % 116.74/116.78 inference(scs_inference,[],[90,20,10,16,2,6,4,5,3])). % 116.74/116.78 cnf(114,plain, % 116.74/116.78 (~E(f2(f4(a1),f4(a1)),f2(f2(f2(a3,f4(a1)),a1),f4(a1)))), % 116.74/116.78 inference(scs_inference,[],[112,2])). % 116.74/116.78 cnf(161,plain, % 116.74/116.78 (E(f2(x1611,f2(f2(a5,a1),f2(a5,a1))),f2(x1611,f2(f2(a1,a5),a1)))), % 116.74/116.78 inference(scs_inference,[],[98,56,3])). % 116.74/116.78 cnf(164,plain, % 116.74/116.78 (E(f2(f2(a5,a5),a1),f2(f2(a5,a1),f2(f2(a1,a5),a1)))), % 116.74/116.78 inference(scs_inference,[],[161,106,3])). % 116.74/116.78 cnf(479,plain, % 116.74/116.78 (~E(f2(a5,x4791),x4791)), % 116.74/116.78 inference(scs_inference,[],[82,4])). % 116.74/116.78 cnf(519,plain, % 116.74/116.78 ($false), % 116.74/116.78 inference(scs_inference,[],[20,92,479,164,114,2,4,3,5]), % 116.74/116.78 ['proof']). % 116.74/116.78 % SZS output end Proof % 116.74/116.78 % Total time :116.080000s %------------------------------------------------------------------------------