TSTP Solution File: NUM024-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM024-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n014.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 : Thu Aug 31 10:20:19 EDT 2023
% Result : Unsatisfiable 0.18s 0.71s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM024-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 11:54:03 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.54 start to proof:theBenchmark
% 0.18/0.70 %-------------------------------------------
% 0.18/0.70 % File :CSE---1.6
% 0.18/0.70 % Problem :theBenchmark
% 0.18/0.70 % Transform :cnf
% 0.18/0.70 % Format :tptp:raw
% 0.18/0.70 % Command :java -jar mcs_scs.jar %d %s
% 0.18/0.70
% 0.18/0.70 % Result :Theorem 0.100000s
% 0.18/0.70 % Output :CNFRefutation 0.100000s
% 0.18/0.70 %-------------------------------------------
% 0.18/0.70 %--------------------------------------------------------------------------
% 0.18/0.70 % File : NUM024-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.18/0.70 % Domain : Number Theory
% 0.18/0.70 % Problem : No number is less than itself
% 0.18/0.70 % Version : [LS74] axioms : Incomplete.
% 0.18/0.70 % English :
% 0.18/0.70
% 0.18/0.70 % Refs : [LS74] Lawrence & Starkey (1974), Experimental Tests of Resol
% 0.18/0.70 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 0.18/0.70 % Source : [SPRFN]
% 0.18/0.70 % Names : ls75 [LS74]
% 0.18/0.70 % : ls75 [WM76]
% 0.18/0.70
% 0.18/0.70 % Status : Unsatisfiable
% 0.18/0.70 % 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
% 0.18/0.70 % Syntax : Number of clauses : 16 ( 8 unt; 0 nHn; 10 RR)
% 0.18/0.70 % Number of literals : 26 ( 0 equ; 11 neg)
% 0.18/0.70 % Maximal clause size : 3 ( 1 avg)
% 0.18/0.70 % Maximal term depth : 4 ( 1 avg)
% 0.18/0.70 % Number of predicates : 2 ( 2 usr; 0 prp; 2-2 aty)
% 0.18/0.70 % Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% 0.18/0.71 % Number of variables : 30 ( 3 sgn)
% 0.18/0.71 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.18/0.71
% 0.18/0.71 % Comments : Surplus transitivity axiom removed and transitivity of less
% 0.18/0.71 % included.
% 0.18/0.71 % Bugfixes : v4.0.0 - Bugfix in NUM001-0.ax
% 0.18/0.71 %--------------------------------------------------------------------------
% 0.18/0.71 %----Include recursive function + and * axioms
% 0.18/0.71 include('Axioms/NUM001-0.ax').
% 0.18/0.71 %----Include recursive function less axioms
% 0.18/0.71 include('Axioms/NUM001-1.ax').
% 0.18/0.71 %--------------------------------------------------------------------------
% 0.18/0.71 cnf(reflexivity,axiom,
% 0.18/0.71 equalish(X,X) ).
% 0.18/0.71
% 0.18/0.71 cnf(symmetry,axiom,
% 0.18/0.71 ( ~ equalish(X,Y)
% 0.18/0.71 | equalish(Y,X) ) ).
% 0.18/0.71
% 0.18/0.71 cnf(transitivity,axiom,
% 0.18/0.71 ( ~ equalish(X,Y)
% 0.18/0.71 | ~ equalish(Y,Z)
% 0.18/0.71 | equalish(X,Z) ) ).
% 0.18/0.71
% 0.18/0.71 cnf(plus_substitution,axiom,
% 0.18/0.71 ( ~ equalish(add(A,B),add(C,B))
% 0.18/0.71 | equalish(A,C) ) ).
% 0.18/0.71
% 0.18/0.71 cnf(commutativity_of_plus,axiom,
% 0.18/0.71 equalish(add(A,B),add(B,A)) ).
% 0.18/0.71
% 0.18/0.71 cnf(impossible_a_is_less_than_itself,hypothesis,
% 0.18/0.71 less(a,a) ).
% 0.18/0.71
% 0.18/0.71 cnf(prove_a_contradiction,negated_conjecture,
% 0.18/0.71 ~ equalish(successor(A),n0) ).
% 0.18/0.71
% 0.18/0.71 %--------------------------------------------------------------------------
% 0.18/0.71 %-------------------------------------------
% 0.18/0.71 % Proof found
% 0.18/0.71 % SZS status Theorem for theBenchmark
% 0.18/0.71 % SZS output start Proof
% 0.18/0.71 %ClaNum:16(EqnAxiom:0)
% 0.18/0.71 %VarNum:60(SingletonVarNum:30)
% 0.18/0.71 %MaxLitNum:3
% 0.18/0.71 %MaxfuncDepth:3
% 0.18/0.71 %SharedTerms:3
% 0.18/0.71 %goalClause: 8
% 0.18/0.71 %singleGoalClaCount:1
% 0.18/0.71 [1]P1(a1,a1)
% 0.18/0.71 [2]P2(x21,x21)
% 0.18/0.71 [3]P2(f3(x31,a2),a2)
% 0.18/0.71 [4]P2(f4(x41,a2),x41)
% 0.18/0.71 [8]~P2(f5(x81),a2)
% 0.18/0.71 [5]P2(f4(x51,x52),f4(x52,x51))
% 0.18/0.71 [6]P2(f4(x61,f5(x62)),f5(f4(x61,x62)))
% 0.18/0.71 [7]P2(f3(x71,f5(x72)),f4(f3(x71,x72),x71))
% 0.18/0.71 [9]~P2(x92,x91)+P2(x91,x92)
% 0.18/0.71 [10]~P2(x101,x102)+P2(f5(x101),f5(x102))
% 0.18/0.71 [11]P2(x111,x112)+~P2(f5(x111),f5(x112))
% 0.18/0.71 [16]~P1(x162,x161)+P2(f4(f5(f6(x161,x162)),x162),x161)
% 0.18/0.71 [15]P2(x151,x152)+~P2(f4(x151,x153),f4(x152,x153))
% 0.18/0.71 [14]P1(x141,x142)+~P2(f4(f5(x143),x141),x142)
% 0.18/0.71 [12]~P2(x121,x123)+P2(x121,x122)+~P2(x123,x122)
% 0.18/0.71 [13]~P1(x133,x132)+P1(x131,x132)+~P1(x131,x133)
% 0.18/0.71 %EqnAxiom
% 0.18/0.71
% 0.18/0.71 %-------------------------------------------
% 0.18/0.71 cnf(18,plain,
% 0.18/0.71 (P1(x181,f4(f5(x182),x181))),
% 0.18/0.71 inference(scs_inference,[],[8,2,9,14])).
% 0.18/0.71 cnf(21,plain,
% 0.18/0.71 (~P2(f4(f5(x211),x212),f4(a2,x212))),
% 0.18/0.71 inference(scs_inference,[],[8,2,9,14,15])).
% 0.18/0.71 cnf(23,plain,
% 0.18/0.71 (~P2(f5(f5(x231)),f5(a2))),
% 0.18/0.71 inference(scs_inference,[],[8,2,9,14,15,11])).
% 0.18/0.71 cnf(25,plain,
% 0.18/0.71 (P2(f5(f4(x251,a2)),f5(x251))),
% 0.18/0.71 inference(scs_inference,[],[8,2,4,9,14,15,11,10])).
% 0.18/0.71 cnf(27,plain,
% 0.18/0.71 (P2(f4(f5(f6(a1,a1)),a1),a1)),
% 0.18/0.71 inference(scs_inference,[],[8,2,1,4,9,14,15,11,10,16])).
% 0.18/0.71 cnf(34,plain,
% 0.18/0.71 (~P2(f5(x341),f3(x342,a2))),
% 0.18/0.71 inference(scs_inference,[],[8,3,9,12])).
% 0.18/0.71 cnf(36,plain,
% 0.18/0.71 (~P1(x361,f4(a2,x361))),
% 0.18/0.71 inference(scs_inference,[],[8,3,21,9,12,16])).
% 0.18/0.71 cnf(44,plain,
% 0.18/0.71 (~P2(f4(f5(x441),f4(f5(x442),x443)),f4(a2,x443))),
% 0.18/0.71 inference(scs_inference,[],[18,36,34,13,9,14])).
% 0.18/0.71 cnf(46,plain,
% 0.18/0.71 (P2(f4(f5(x461),x462),f5(f4(x462,x461)))),
% 0.18/0.71 inference(scs_inference,[],[5,6,18,36,34,13,9,14,12])).
% 0.18/0.71 cnf(53,plain,
% 0.18/0.71 (P2(f4(x531,x532),f4(x532,x531))),
% 0.18/0.71 inference(rename_variables,[],[5])).
% 0.18/0.71 cnf(55,plain,
% 0.18/0.71 (P1(x551,f4(x551,f5(x552)))),
% 0.18/0.71 inference(scs_inference,[],[7,5,53,44,9,12,14])).
% 0.18/0.71 cnf(60,plain,
% 0.18/0.71 (P1(x601,f4(f5(x602),f4(x601,f5(x603))))),
% 0.18/0.71 inference(scs_inference,[],[18,55,13])).
% 0.18/0.71 cnf(76,plain,
% 0.18/0.71 (~P1(f4(f5(x761),f4(x762,f5(x763))),f4(a2,x762))),
% 0.18/0.71 inference(scs_inference,[],[60,36,13])).
% 0.18/0.71 cnf(79,plain,
% 0.18/0.71 (P2(x791,f4(x791,a2))),
% 0.18/0.71 inference(scs_inference,[],[4,60,36,13,9])).
% 0.18/0.71 cnf(81,plain,
% 0.18/0.71 (P1(a2,f5(x811))),
% 0.18/0.71 inference(scs_inference,[],[4,60,36,13,9,14])).
% 0.18/0.71 cnf(88,plain,
% 0.18/0.71 (~P2(f4(x881,f5(x882)),f4(a2,x881))),
% 0.18/0.71 inference(scs_inference,[],[21,5,76,55,13,12])).
% 0.18/0.71 cnf(94,plain,
% 0.18/0.71 (P1(a2,f4(f5(x941),f5(x942)))),
% 0.18/0.71 inference(scs_inference,[],[18,81,13])).
% 0.18/0.71 cnf(100,plain,
% 0.18/0.71 (P2(f5(f4(x1001,x1002)),f4(x1001,f5(x1002)))),
% 0.18/0.71 inference(scs_inference,[],[3,18,6,79,81,13,12,9])).
% 0.18/0.71 cnf(102,plain,
% 0.18/0.71 (~P1(f4(f5(x1021),f5(x1022)),f4(a2,a2))),
% 0.18/0.71 inference(scs_inference,[],[94,36,13])).
% 0.18/0.71 cnf(105,plain,
% 0.18/0.71 (~P2(f4(f5(x1051),f4(f5(x1052),f5(x1053))),f4(a2,a2))),
% 0.18/0.71 inference(scs_inference,[],[94,36,13,14])).
% 0.18/0.71 cnf(112,plain,
% 0.18/0.71 (P2(f5(f4(x1121,x1122)),f5(f4(x1122,x1121)))),
% 0.18/0.71 inference(scs_inference,[],[4,23,5,88,94,36,13,14,12,9,10])).
% 0.18/0.71 cnf(116,plain,
% 0.18/0.71 (~P2(f4(f5(f5(x1161)),x1162),f4(f5(a2),x1162))),
% 0.18/0.71 inference(scs_inference,[],[4,23,5,88,94,36,13,14,12,9,10,11,15])).
% 0.18/0.71 cnf(121,plain,
% 0.18/0.71 (P1(f5(x1211),f5(f4(f5(x1212),x1211)))),
% 0.18/0.71 inference(scs_inference,[],[18,6,102,13,14])).
% 0.18/0.71 cnf(124,plain,
% 0.18/0.71 (~P2(f4(f4(f5(x1241),f5(x1242)),f5(x1243)),f4(a2,a2))),
% 0.18/0.71 inference(scs_inference,[],[18,6,5,105,102,13,14,12])).
% 0.18/0.71 cnf(127,plain,
% 0.18/0.71 (P2(f5(f4(x1271,x1272)),f4(f5(x1272),x1271))),
% 0.18/0.71 inference(scs_inference,[],[18,6,5,46,105,102,13,14,12,9])).
% 0.18/0.71 cnf(137,plain,
% 0.18/0.71 (P1(x1371,f5(f4(x1371,x1372)))),
% 0.18/0.71 inference(scs_inference,[],[25,18,100,124,46,60,13,12,9,14])).
% 0.18/0.71 cnf(147,plain,
% 0.18/0.71 (~P1(x1471,f4(x1471,a2))),
% 0.18/0.71 inference(scs_inference,[],[5,25,21,121,36,13,12,9,16])).
% 0.18/0.71 cnf(161,plain,
% 0.18/0.71 (P2(f5(f5(f4(x1611,a2))),f5(f5(x1611)))),
% 0.18/0.71 inference(scs_inference,[],[6,25,21,18,116,147,13,14,12,9,10])).
% 0.18/0.71 cnf(170,plain,
% 0.18/0.71 (P1(x1701,f4(f4(f5(x1702),x1701),a2))),
% 0.18/0.71 inference(scs_inference,[],[18,137,79,13,14])).
% 0.18/0.71 cnf(175,plain,
% 0.18/0.71 (P2(f4(x1751,f5(a2)),f5(x1751))),
% 0.18/0.71 inference(scs_inference,[],[6,27,25,18,137,79,13,14,9,12])).
% 0.18/0.71 cnf(181,plain,
% 0.18/0.71 (~P2(f4(f5(x1811),f5(x1812)),f4(a2,a2))),
% 0.18/0.71 inference(scs_inference,[],[147,81,13,14])).
% 0.18/0.71 cnf(194,plain,
% 0.18/0.71 (~P2(a1,f4(a2,a1))),
% 0.18/0.71 inference(scs_inference,[],[27,21,161,175,14,9,12])).
% 0.18/0.71 cnf(197,plain,
% 0.18/0.71 (~P1(f4(f5(x1971),x1972),x1972)),
% 0.18/0.71 inference(scs_inference,[],[27,21,161,175,170,147,14,9,12,13])).
% 0.18/0.71 cnf(207,plain,
% 0.18/0.71 (P2(f5(f4(f4(x2071,x2072),a2)),f5(f4(x2072,x2071)))),
% 0.18/0.71 inference(scs_inference,[],[25,18,112,197,181,13,14,9,12])).
% 0.18/0.71 cnf(218,plain,
% 0.18/0.71 (P2(f4(f4(x2181,x2182),a2),f4(x2182,x2181))),
% 0.18/0.71 inference(scs_inference,[],[207,11])).
% 0.18/0.71 cnf(244,plain,
% 0.18/0.71 ($false),
% 0.18/0.71 inference(scs_inference,[],[25,127,218,194,9,12,15]),
% 0.18/0.71 ['proof']).
% 0.18/0.71 % SZS output end Proof
% 0.18/0.71 % Total time :0.100000s
%------------------------------------------------------------------------------