%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWX186+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n008.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 : Tue May 5 06:57:06 PM UTC 2026 % Result : Theorem 0.54s 0.68s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX186+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.14/0.33 % Computer : n008.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 300 % 0.14/0.33 % DateTime : Tue May 5 09:36:43 EDT 2026 % 0.14/0.33 % CPUTime : % 0.52/0.57 start to proof:theBenchmark % 0.54/0.67 %------------------------------------------- % 0.54/0.67 % File :CSE---1.7 % 0.54/0.67 % Problem :theBenchmark % 0.54/0.67 % Transform :cnf % 0.54/0.67 % Format :tptp:raw % 0.54/0.67 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.67 % 0.54/0.67 % Result :Theorem 0.070000s % 0.54/0.67 % Output :CNFRefutation 0.070000s % 0.54/0.67 %------------------------------------------- % 0.54/0.67 %------------------------------------------------------------------------------ % 0.54/0.67 % File : SWX186+1 : TPTP v9.3.0. Released v9.3.0. % 0.54/0.67 % Domain : Software Verification % 0.54/0.67 % Problem : A faulty property of the function drop % 0.54/0.67 % Version : Especial. % 0.54/0.67 % English : % 0.54/0.67 % 0.54/0.67 % Refs : [CST26] Claessen et al. (2026), Email to Geoff Sutcliffe % 0.54/0.67 % Source : [CST26] % 0.54/0.67 % Names : Definitions_prop_drop_inj2.p [CST26] % 0.54/0.67 % 0.54/0.67 % Status : Theorem % 0.54/0.67 % Rating : ? v9.3.0 % 0.54/0.67 % Syntax : Number of formulae : 9 ( 8 unt; 0 def) % 0.54/0.67 % Number of atoms : 10 ( 10 equ) % 0.54/0.68 % Maximal formula atoms : 2 ( 1 avg) % 0.54/0.68 % Number of connectives : 4 ( 3 ~; 0 |; 0 &) % 0.54/0.68 % ( 0 <=>; 1 =>; 0 <=; 0 <~>) % 0.54/0.68 % Maximal formula depth : 6 ( 3 avg) % 0.54/0.68 % Maximal term depth : 3 ( 1 avg) % 0.54/0.68 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 0.54/0.68 % Number of functors : 8 ( 8 usr; 2 con; 0-2 aty) % 0.54/0.68 % Number of variables : 16 ( 13 !; 3 ?) % 0.54/0.68 % SPC : FOF_THM_RFO_PEQ % 0.54/0.68 % 0.54/0.68 % Comments : % 0.54/0.68 %------------------------------------------------------------------------------ % 0.54/0.68 fof(axiom_001,axiom, % 0.54/0.68 ! [X,X2] : head(cons(X,X2)) = X ). % 0.54/0.68 % 0.54/0.68 fof(axiom_002,axiom, % 0.54/0.68 ! [X,X2] : tail(cons(X,X2)) = X2 ). % 0.54/0.68 % 0.54/0.68 fof(axiom_003,axiom, % 0.54/0.68 ! [X,X2] : nil != cons(X,X2) ). % 0.54/0.68 % 0.54/0.68 fof(axiom_004,axiom, % 0.54/0.68 ! [X] : proj1S(s(X)) = X ). % 0.54/0.68 % 0.54/0.68 fof(axiom_005,axiom, % 0.54/0.68 ! [X] : s(X) != z ). % 0.54/0.68 % 0.54/0.68 fof(axiom_006,axiom, % 0.54/0.68 ! [Z] : drop(s(Z),nil) = nil ). % 0.54/0.68 % 0.54/0.68 fof(axiom_007,axiom, % 0.54/0.68 ! [Z,X2,X3] : drop(s(Z),cons(X2,X3)) = drop(Z,X3) ). % 0.54/0.68 % 0.54/0.68 fof(axiom_008,axiom, % 0.54/0.68 ! [Y] : drop(z,Y) = Y ). % 0.54/0.68 % 0.54/0.68 fof(goal_009,conjecture, % 0.54/0.68 ? [N,Xs,Ys] : % 0.54/0.68 ~ ( drop(N,Xs) = drop(N,Ys) % 0.54/0.68 => Xs = Ys ) ). % 0.54/0.68 % 0.54/0.68 %------------------------------------------------------------------------------ % 0.54/0.68 %------------------------------------------- % 0.54/0.68 % Proof found % 0.54/0.68 % SZS status Theorem for theBenchmark % 0.54/0.68 % SZS output start Proof % 0.54/0.68 %ClaNum:20(EqnAxiom:11) % 0.54/0.68 %VarNum:25(SingletonVarNum:16) % 0.54/0.68 %MaxLitNum:2 % 0.54/0.68 %MaxfuncDepth:2 % 0.54/0.68 %SharedTerms:2 % 0.54/0.68 %goalClause: 20 % 0.54/0.68 [13]E(f3(a7,x131),x131) % 0.54/0.68 [18]~E(f1(x181),a7) % 0.54/0.68 [12]E(f2(f1(x121)),x121) % 0.54/0.68 [14]E(f3(f1(x141),a5),a5) % 0.54/0.68 [19]~E(f4(x191,x192),a5) % 0.54/0.68 [15]E(f6(f4(x151,x152)),x151) % 0.54/0.68 [16]E(f8(f4(x161,x162)),x162) % 0.54/0.68 [17]E(f3(f1(x171),f4(x172,x173)),f3(x171,x173)) % 0.54/0.68 [20]E(x201,x202)+~E(f3(x203,x201),f3(x203,x202)) % 0.54/0.68 %EqnAxiom % 0.54/0.68 [1]E(x11,x11) % 0.54/0.68 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.68 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.68 [4]~E(x41,x42)+E(f1(x41),f1(x42)) % 0.54/0.68 [5]~E(x51,x52)+E(f2(x51),f2(x52)) % 0.54/0.68 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 0.54/0.68 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 0.54/0.68 [8]~E(x81,x82)+E(f4(x81,x83),f4(x82,x83)) % 0.54/0.68 [9]~E(x91,x92)+E(f4(x93,x91),f4(x93,x92)) % 0.54/0.68 [10]~E(x101,x102)+E(f8(x101),f8(x102)) % 0.54/0.68 [11]~E(x111,x112)+E(f6(x111),f6(x112)) % 0.54/0.68 % 0.54/0.68 %------------------------------------------- % 0.54/0.68 cnf(25,plain, % 0.54/0.68 (E(x251,f3(a7,x251))), % 0.54/0.68 inference(scs_inference,[],[13,2])). % 0.54/0.68 cnf(28,plain, % 0.54/0.68 (E(f3(x281,x282),f3(f1(x281),f4(x283,x282)))), % 0.54/0.68 inference(scs_inference,[],[17,2])). % 0.54/0.68 cnf(65,plain, % 0.54/0.68 (~E(f3(x651,a5),f3(x651,f4(x652,x653)))), % 0.54/0.68 inference(scs_inference,[],[19,2,20])). % 0.54/0.68 cnf(67,plain, % 0.54/0.68 ($false), % 0.54/0.68 inference(scs_inference,[],[65,28,25,7,3]), % 0.54/0.68 ['proof']). % 0.54/0.68 % SZS output end Proof % 0.54/0.68 % Total time :0.070000s %------------------------------------------------------------------------------