%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : NUM024-1 : TPTP v8.2.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 12:23:00 EDT 2024
% Result : Unsatisfiable 17.40s 17.51s
% Output : CNFRefutation 17.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM024-1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Jun 22 22:46:54 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.21/0.56 start to proof:theBenchmark
% 17.40/17.51 %-------------------------------------------
% 17.40/17.51 % File :CSE---1.7
% 17.40/17.51 % Problem :theBenchmark
% 17.40/17.51 % Transform :cnf
% 17.40/17.51 % Format :tptp:raw
% 17.40/17.51 % Command :java -jar mcs_scs.jar %d %s
% 17.40/17.51
% 17.40/17.51 % Result :Theorem 16.910000s
% 17.40/17.51 % Output :CNFRefutation 16.910000s
% 17.40/17.51 %-------------------------------------------
% 17.40/17.51 %--------------------------------------------------------------------------
% 17.40/17.51 % File : NUM024-1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 17.40/17.51 % Domain : Number Theory
% 17.40/17.51 % Problem : No number is less than itself
% 17.40/17.51 % Version : [LS74] axioms : Incomplete.
% 17.40/17.51 % English :
% 17.40/17.51
% 17.40/17.51 % Refs : [LS74] Lawrence & Starkey (1974), Experimental Tests of Resol
% 17.40/17.51 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 17.40/17.51 % Source : [SPRFN]
% 17.40/17.51 % Names : ls75 [LS74]
% 17.40/17.51 % : ls75 [WM76]
% 17.40/17.51
% 17.40/17.51 % Status : Unsatisfiable
% 17.40/17.51 % Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.08 v5.1.0, 0.12 v5.0.0, 0.00 v4.1.0, 0.07 v4.0.1, 0.00 v4.0.0
% 17.40/17.51 % Syntax : Number of clauses : 16 ( 8 unt; 0 nHn; 10 RR)
% 17.40/17.51 % Number of literals : 26 ( 0 equ; 11 neg)
% 17.40/17.51 % Maximal clause size : 3 ( 1 avg)
% 17.40/17.51 % Maximal term depth : 4 ( 1 avg)
% 17.40/17.51 % Number of predicates : 2 ( 2 usr; 0 prp; 2-2 aty)
% 17.40/17.51 % Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% 17.40/17.51 % Number of variables : 30 ( 3 sgn)
% 17.40/17.51 % SPC : CNF_UNS_RFO_NEQ_HRN
% 17.40/17.51
% 17.40/17.51 % Comments : Surplus transitivity axiom removed and transitivity of less
% 17.40/17.51 % included.
% 17.40/17.51 % Bugfixes : v4.0.0 - Bugfix in NUM001-0.ax
% 17.40/17.51 %--------------------------------------------------------------------------
% 17.40/17.51 %----Include recursive function + and * axioms
% 17.40/17.51 include('Axioms/NUM001-0.ax').
% 17.40/17.51 %----Include recursive function less axioms
% 17.40/17.51 include('Axioms/NUM001-1.ax').
% 17.40/17.51 %--------------------------------------------------------------------------
% 17.40/17.51 cnf(reflexivity,axiom,
% 17.40/17.51 equalish(X,X) ).
% 17.40/17.51
% 17.40/17.51 cnf(symmetry,axiom,
% 17.40/17.51 ( ~ equalish(X,Y)
% 17.40/17.51 | equalish(Y,X) ) ).
% 17.40/17.51
% 17.40/17.51 cnf(transitivity,axiom,
% 17.40/17.51 ( ~ equalish(X,Y)
% 17.40/17.51 | ~ equalish(Y,Z)
% 17.40/17.51 | equalish(X,Z) ) ).
% 17.40/17.51
% 17.40/17.51 cnf(plus_substitution,axiom,
% 17.40/17.51 ( ~ equalish(add(A,B),add(C,B))
% 17.40/17.51 | equalish(A,C) ) ).
% 17.40/17.51
% 17.40/17.51 cnf(commutativity_of_plus,axiom,
% 17.40/17.51 equalish(add(A,B),add(B,A)) ).
% 17.40/17.51
% 17.40/17.51 cnf(impossible_a_is_less_than_itself,hypothesis,
% 17.40/17.51 less(a,a) ).
% 17.40/17.51
% 17.40/17.51 cnf(prove_a_contradiction,negated_conjecture,
% 17.40/17.51 ~ equalish(successor(A),n0) ).
% 17.40/17.51
% 17.40/17.51 %--------------------------------------------------------------------------
% 17.40/17.51 %-------------------------------------------
% 17.40/17.51 % Proof found
% 17.40/17.51 % SZS status Theorem for theBenchmark
% 17.40/17.51 % SZS output start Proof
% 17.40/17.52 %ClaNum:16(EqnAxiom:0)
% 17.40/17.52 %VarNum:60(SingletonVarNum:30)
% 17.40/17.52 %MaxLitNum:3
% 17.40/17.52 %MaxfuncDepth:3
% 17.40/17.52 %SharedTerms:3
% 17.40/17.52 %goalClause: 8
% 17.40/17.52 %singleGoalClaCount:1
% 17.40/17.52 [1]P1(a1,a1)
% 17.40/17.52 [2]P2(x21,x21)
% 17.40/17.52 [3]P2(f3(x31,a2),a2)
% 17.40/17.52 [4]P2(f4(x41,a2),x41)
% 17.40/17.52 [8]~P2(f5(x81),a2)
% 17.40/17.52 [5]P2(f4(x51,x52),f4(x52,x51))
% 17.40/17.52 [6]P2(f4(x61,f5(x62)),f5(f4(x61,x62)))
% 17.40/17.52 [7]P2(f3(x71,f5(x72)),f4(f3(x71,x72),x71))
% 17.40/17.52 [9]~P2(x92,x91)+P2(x91,x92)
% 17.40/17.52 [10]~P2(x101,x102)+P2(f5(x101),f5(x102))
% 17.40/17.52 [11]P2(x111,x112)+~P2(f5(x111),f5(x112))
% 17.40/17.52 [16]~P1(x162,x161)+P2(f4(f5(f6(x161,x162)),x162),x161)
% 17.40/17.52 [15]P2(x151,x152)+~P2(f4(x151,x153),f4(x152,x153))
% 17.40/17.52 [14]P1(x141,x142)+~P2(f4(f5(x143),x141),x142)
% 17.40/17.52 [12]~P2(x121,x123)+P2(x121,x122)+~P2(x123,x122)
% 17.40/17.52 [13]~P1(x133,x132)+P1(x131,x132)+~P1(x131,x133)
% 17.40/17.52 %EqnAxiom
% 17.40/17.52
% 17.40/17.52 %-------------------------------------------
% 17.40/17.52 cnf(17,plain,
% 17.40/17.52 (~P2(a2,f5(x171))),
% 17.40/17.52 inference(scs_inference,[],[8,9])).
% 17.40/17.52 cnf(22,plain,
% 17.40/17.52 (~P1(f4(f5(x221),x222),x223)+P1(x222,x223)),
% 17.40/17.52 inference(scs_inference,[],[8,2,9,14,13])).
% 17.40/17.52 cnf(48,plain,
% 17.40/17.52 (~P2(f5(f5(x481)),f5(a2))),
% 17.40/17.52 inference(scs_inference,[],[17,11,9])).
% 17.40/17.52 cnf(72,plain,
% 17.40/17.52 (P2(f5(x721),f5(f4(x721,a2)))),
% 17.40/17.52 inference(scs_inference,[],[4,9,10])).
% 17.40/17.52 cnf(73,plain,
% 17.40/17.52 (P2(x731,f4(x731,a2))),
% 17.40/17.52 inference(scs_inference,[],[72,11])).
% 17.40/17.52 cnf(794,plain,
% 17.40/17.52 (~P2(f4(f5(x7941),x7942),f4(a2,x7942))),
% 17.40/17.52 inference(scs_inference,[],[48,10,15])).
% 17.40/17.52 cnf(796,plain,
% 17.40/17.52 (~P2(f4(f5(x7961),x7962),f4(a2,x7962))),
% 17.40/17.52 inference(rename_variables,[],[794])).
% 17.40/17.52 cnf(800,plain,
% 17.40/17.52 (~P2(f4(a2,x8001),f4(f5(x8002),x8001))),
% 17.40/17.52 inference(scs_inference,[],[794,796,16,22,9])).
% 17.40/17.52 cnf(1089,plain,
% 17.40/17.52 (P2(a1,f4(f5(f6(a1,a1)),a1))),
% 17.40/17.52 inference(scs_inference,[],[1,16,9])).
% 17.40/17.52 cnf(1093,plain,
% 17.40/17.52 (~P2(a1,f4(a2,a1))),
% 17.40/17.52 inference(scs_inference,[],[800,1089,12,9])).
% 17.40/17.52 cnf(1305,plain,
% 17.40/17.52 ($false),
% 17.40/17.52 inference(scs_inference,[],[1093,73,5,12]),
% 17.40/17.52 ['proof']).
% 17.50/17.53 % SZS output end Proof
% 17.50/17.53 % Total time :16.910000s
%------------------------------------------------------------------------------