%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : NUM021-1 : 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 : n032.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 0.93s 1.09s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM021-1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 0.00/0.09 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Sat Jun 22 21:15:08 EDT 2024
% 0.08/0.28 % CPUTime :
% 0.14/0.46 start to proof:theBenchmark
% 0.93/1.08 %-------------------------------------------
% 0.93/1.08 % File :CSE---1.7
% 0.93/1.08 % Problem :theBenchmark
% 0.93/1.08 % Transform :cnf
% 0.93/1.08 % Format :tptp:raw
% 0.93/1.08 % Command :java -jar mcs_scs.jar %d %s
% 0.93/1.08
% 0.93/1.08 % Result :Theorem 0.590000s
% 0.93/1.08 % Output :CNFRefutation 0.590000s
% 0.93/1.08 %-------------------------------------------
% 0.93/1.08 %--------------------------------------------------------------------------
% 0.93/1.08 % File : NUM021-1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 0.93/1.09 % Domain : Number Theory
% 0.93/1.09 % Problem : If a <= b < c, then c cannot divide a
% 0.93/1.09 % Version : [LS74] axioms : Incomplete.
% 0.93/1.09 % English :
% 0.93/1.09
% 0.93/1.09 % Refs : [LS74] Lawrence & Starkey (1974), Experimental Tests of Resol
% 0.93/1.09 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 0.93/1.09 % Source : [SPRFN]
% 0.93/1.09 % Names : ls65 [LS74]
% 0.93/1.09 % : ls65 [WM76]
% 0.93/1.09
% 0.93/1.09 % Status : Unsatisfiable
% 0.93/1.09 % Rating : 0.00 v7.5.0, 0.17 v7.4.0, 0.00 v7.0.0, 0.12 v6.3.0, 0.14 v6.2.0, 0.00 v5.0.0, 0.07 v4.1.0, 0.00 v4.0.0
% 0.93/1.09 % Syntax : Number of clauses : 19 ( 9 unt; 1 nHn; 14 RR)
% 0.93/1.09 % Number of literals : 32 ( 0 equ; 14 neg)
% 0.93/1.09 % Maximal clause size : 3 ( 1 avg)
% 0.93/1.09 % Maximal term depth : 4 ( 1 avg)
% 0.93/1.09 % Number of predicates : 3 ( 3 usr; 0 prp; 2-2 aty)
% 0.93/1.09 % Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% 0.93/1.09 % Number of variables : 31 ( 3 sgn)
% 0.93/1.09 % SPC : CNF_UNS_RFO_NEQ_NHN
% 0.93/1.09
% 0.93/1.09 % Comments : Surplus transitivity axiom removed.
% 0.93/1.09 % : This is dumb, because there is no need for the clause
% 0.93/1.09 % prove_a_contradiction.
% 0.93/1.09 % Bugfixes : v4.0.0 - Bugfix in NUM001-0.ax
% 0.93/1.09 %--------------------------------------------------------------------------
% 0.93/1.09 %----Include recursive function + and * axioms
% 0.93/1.09 include('Axioms/NUM001-0.ax').
% 0.93/1.09 %----Include recursive function less axioms
% 0.93/1.09 include('Axioms/NUM001-1.ax').
% 0.93/1.09 %----Include recursive function divides axioms
% 0.93/1.09 include('Axioms/NUM001-2.ax').
% 0.93/1.09 %--------------------------------------------------------------------------
% 0.93/1.09 cnf(reflexivity,axiom,
% 0.93/1.09 equalish(X,X) ).
% 0.93/1.09
% 0.93/1.09 cnf(symmetry,axiom,
% 0.93/1.09 ( ~ equalish(X,Y)
% 0.93/1.09 | equalish(Y,X) ) ).
% 0.93/1.09
% 0.93/1.09 cnf(transitivity,axiom,
% 0.93/1.09 ( ~ equalish(X,Y)
% 0.93/1.09 | ~ equalish(Y,Z)
% 0.93/1.09 | equalish(X,Z) ) ).
% 0.93/1.09
% 0.93/1.09 cnf(b_less_than_c,hypothesis,
% 0.93/1.09 less(b,c) ).
% 0.93/1.09
% 0.93/1.09 cnf(b_greater_equal_a,hypothesis,
% 0.93/1.09 ~ less(b,a) ).
% 0.93/1.09
% 0.93/1.09 cnf(impossible_c_divides_a,negated_conjecture,
% 0.93/1.09 divides(c,a) ).
% 0.93/1.09
% 0.93/1.09 cnf(prove_a_contradiction,negated_conjecture,
% 0.93/1.09 ~ equalish(successor(A),n0) ).
% 0.93/1.09
% 0.93/1.09 %--------------------------------------------------------------------------
% 0.93/1.09 %-------------------------------------------
% 0.93/1.09 % Proof found
% 0.93/1.09 % SZS status Theorem for theBenchmark
% 0.93/1.09 % SZS output start Proof
% 0.93/1.09 %ClaNum:19(EqnAxiom:0)
% 0.93/1.09 %VarNum:64(SingletonVarNum:31)
% 0.93/1.09 %MaxLitNum:3
% 0.93/1.09 %MaxfuncDepth:3
% 0.93/1.09 %SharedTerms:7
% 0.93/1.09 %goalClause: 2 9
% 0.93/1.09 %singleGoalClaCount:2
% 0.93/1.09 [1]P1(a1,a4)
% 0.93/1.09 [2]P2(a4,a2)
% 0.93/1.09 [8]~P1(a1,a2)
% 0.93/1.09 [3]P3(x31,x31)
% 0.93/1.09 [4]P3(f6(x41,a5),a5)
% 0.93/1.09 [5]P3(f3(x51,a5),x51)
% 0.93/1.09 [9]~P3(f7(x91),a5)
% 0.93/1.09 [6]P3(f3(x61,f7(x62)),f7(f3(x61,x62)))
% 0.93/1.09 [7]P3(f6(x71,f7(x72)),f3(f6(x71,x72),x71))
% 0.93/1.09 [10]~P3(x102,x101)+P3(x101,x102)
% 0.93/1.09 [11]~P3(x111,x112)+P2(x111,x112)
% 0.93/1.09 [12]~P1(x121,x122)+P2(x121,x122)
% 0.93/1.09 [13]~P3(x131,x132)+P3(f7(x131),f7(x132))
% 0.93/1.09 [15]P3(x151,x152)+~P3(f7(x151),f7(x152))
% 0.93/1.09 [19]~P1(x192,x191)+P3(f3(f7(f8(x191,x192)),x192),x191)
% 0.93/1.09 [18]P1(x181,x182)+~P3(f3(f7(x183),x181),x182)
% 0.93/1.09 [14]P1(x141,x142)+~P2(x141,x142)+P3(x141,x142)
% 0.93/1.09 [16]~P3(x161,x163)+P3(x161,x162)+~P3(x163,x162)
% 0.93/1.09 [17]~P1(x173,x172)+P1(x171,x172)+~P1(x171,x173)
% 0.93/1.09 %EqnAxiom
% 0.93/1.09
% 0.93/1.09 %-------------------------------------------
% 0.93/1.09 cnf(27,plain,
% 0.93/1.09 (P3(a4,a2)+P1(a4,a2)),
% 0.93/1.09 inference(scs_inference,[],[2,9,3,1,10,18,17,14])).
% 0.93/1.09 cnf(69,plain,
% 0.93/1.09 (P1(a4,a2)+P3(f7(a4),f7(a2))),
% 0.93/1.09 inference(scs_inference,[],[27,13])).
% 0.93/1.09 cnf(71,plain,
% 0.93/1.09 (P3(f7(a4),f7(a2))),
% 0.93/1.09 inference(scs_inference,[],[1,8,69,17])).
% 0.93/1.09 cnf(72,plain,
% 0.93/1.09 (P3(a4,a2)),
% 0.93/1.09 inference(scs_inference,[],[71,15])).
% 0.93/1.09 cnf(346,plain,
% 0.93/1.09 (~P3(f3(f7(x3461),a1),a4)),
% 0.93/1.09 inference(scs_inference,[],[8,72,18,16])).
% 0.93/1.09 cnf(349,plain,
% 0.93/1.09 ($false),
% 0.93/1.09 inference(scs_inference,[],[346,1,19]),
% 0.93/1.09 ['proof']).
% 0.93/1.09 % SZS output end Proof
% 0.93/1.09 % Total time :0.590000s
%------------------------------------------------------------------------------