%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG005-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:49:06 AM UTC 2026
% Result : Unsatisfiable 2.62s 1.21s
% Output : CNFRefutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 79 ( 79 unt; 0 def)
% Number of atoms : 79 ( 78 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 199 ( 19 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(set_difference_1,axiom,
! [VAR_0,VAR_1] : difference(VAR_0,difference(VAR_1,VAR_0)) = VAR_0,
file('theBenchmark.p',set_difference_1) ).
cnf(c_1,plain,
difference(A,difference(B,A)) = A,
inference(clausify,[status(thm)],[set_difference_1]) ).
fof(set_difference_2,axiom,
! [VAR_0,VAR_1] : difference(VAR_0,difference(VAR_0,VAR_1)) = difference(VAR_1,difference(VAR_1,VAR_0)),
file('theBenchmark.p',set_difference_2) ).
cnf(c_2,plain,
difference(A,difference(A,B)) = difference(B,difference(B,A)),
inference(clausify,[status(thm)],[set_difference_2]) ).
fof(set_difference_3,axiom,
! [VAR_0,VAR_1,VAR_2] : difference(difference(VAR_0,VAR_1),VAR_2) = difference(difference(VAR_0,VAR_2),difference(VAR_1,VAR_2)),
file('theBenchmark.p',set_difference_3) ).
cnf(c_3,plain,
difference(difference(A,B),C) = difference(difference(A,C),difference(B,C)),
inference(clausify,[status(thm)],[set_difference_3]) ).
cnf(c_4,plain,
difference(difference(A,B),difference(C,B)) = difference(difference(A,C),B),
inference(copy,[status(thm)],[c_3]) ).
fof(intersection,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = difference(VAR_0,difference(VAR_0,VAR_1)),
file('theBenchmark.p',intersection) ).
cnf(c_5,plain,
multiply(A,B) = difference(A,difference(A,B)),
inference(clausify,[status(thm)],[intersection]) ).
fof(prove_associativity_of_multiply,axiom,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('theBenchmark.p',prove_associativity_of_multiply) ).
cnf(c_6,plain,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
inference(clausify,[status(thm)],[prove_associativity_of_multiply]) ).
cnf(c_653,plain,
multiply(difference(a,difference(a,b)),c) != multiply(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_5,c_6]) ).
cnf(c_654,plain,
difference(difference(a,difference(a,b)),difference(difference(a,difference(a,b)),c)) != multiply(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_5,c_653]) ).
cnf(c_655,plain,
difference(c,difference(c,difference(a,difference(a,b)))) != multiply(a,multiply(b,c)),
inference(paramod,[status(thm)],[c_2,c_654]) ).
cnf(c_656,plain,
difference(c,difference(c,difference(a,difference(a,b)))) != multiply(a,difference(b,difference(b,c))),
inference(paramod,[status(thm)],[c_5,c_655]) ).
cnf(c_7,plain,
difference(c,difference(c,difference(a,difference(a,b)))) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(paramod,[status(thm)],[c_5,c_656]) ).
cnf(c_8,plain,
difference(difference(A,B),B) = difference(A,B),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_657,plain,
difference(A,A) = difference(difference(B,A),difference(difference(B,A),A)),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_658,plain,
difference(A,A) = difference(difference(B,A),difference(B,A)),
inference(paramod,[status(thm)],[c_8,c_657]) ).
cnf(c_659,plain,
difference(A,A) = difference(difference(B,B),A),
inference(paramod,[status(thm)],[c_4,c_658]) ).
cnf(c_10,plain,
difference(difference(A,A),B) = difference(B,B),
inference(copy,[status(thm)],[c_659]) ).
cnf(c_660,plain,
difference(A,difference(B,difference(C,A))) = difference(difference(A,B),difference(C,A)),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_12,plain,
difference(difference(A,B),difference(C,A)) = difference(A,difference(B,difference(C,A))),
inference(copy,[status(thm)],[c_660]) ).
cnf(c_18,plain,
difference(difference(A,difference(B,C)),difference(difference(D,B),C)) = difference(difference(A,difference(D,C)),difference(B,C)),
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_661,plain,
difference(difference(A,B),difference(C,B)) = difference(difference(difference(A,B),C),B),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_662,plain,
difference(difference(A,C),B) = difference(difference(difference(A,B),C),B),
inference(paramod,[status(thm)],[c_4,c_661]) ).
cnf(c_20,plain,
difference(difference(difference(A,B),C),B) = difference(difference(A,C),B),
inference(copy,[status(thm)],[c_662]) ).
cnf(c_663,plain,
difference(difference(A,difference(B,B)),difference(A,difference(B,B))) = difference(B,B),
inference(paramod,[status(thm)],[c_10,c_1]) ).
cnf(c_21,plain,
difference(difference(A,A),difference(B,B)) = difference(B,B),
inference(paramod,[status(thm)],[c_4,c_663]) ).
cnf(c_664,plain,
difference(difference(A,A),difference(B,B)) = difference(difference(B,B),difference(difference(B,B),difference(A,A))),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_665,plain,
difference(B,B) = difference(difference(B,B),difference(difference(B,B),difference(A,A))),
inference(paramod,[status(thm)],[c_21,c_664]) ).
cnf(c_666,plain,
difference(B,B) = difference(difference(B,B),difference(A,A)),
inference(paramod,[status(thm)],[c_21,c_665]) ).
cnf(c_32,plain,
difference(A,A) = difference(B,B),
inference(paramod,[status(thm)],[c_21,c_666]) ).
cnf(c_35,plain,
difference(A,difference(B,B)) = A,
inference(paramod,[status(thm)],[c_32,c_1]) ).
cnf(c_667,plain,
difference(A,A) = difference(difference(B,B),C),
inference(paramod,[status(thm)],[c_32,c_4]) ).
cnf(c_37,plain,
difference(difference(A,A),B) = difference(C,C),
inference(copy,[status(thm)],[c_667]) ).
cnf(c_668,plain,
difference(A,A) = difference(difference(B,C),B),
inference(paramod,[status(thm)],[c_37,c_4]) ).
cnf(c_40,plain,
difference(difference(A,B),A) = difference(C,C),
inference(copy,[status(thm)],[c_668]) ).
cnf(c_45,plain,
difference(A,difference(difference(B,C),B)) = A,
inference(paramod,[status(thm)],[c_40,c_1]) ).
cnf(c_669,plain,
difference(difference(A,B),difference(C,C)) = difference(A,difference(A,difference(A,B))),
inference(paramod,[status(thm)],[c_40,c_2]) ).
cnf(c_670,plain,
difference(A,B) = difference(A,difference(A,difference(A,B))),
inference(paramod,[status(thm)],[c_35,c_669]) ).
cnf(c_46,plain,
difference(A,difference(A,difference(A,B))) = difference(A,B),
inference(copy,[status(thm)],[c_670]) ).
cnf(c_671,plain,
difference(difference(A,B),difference(C,C)) = difference(difference(A,difference(B,D)),B),
inference(paramod,[status(thm)],[c_40,c_4]) ).
cnf(c_672,plain,
difference(A,B) = difference(difference(A,difference(B,D)),B),
inference(paramod,[status(thm)],[c_35,c_671]) ).
cnf(c_48,plain,
difference(difference(A,difference(B,C)),B) = difference(A,B),
inference(copy,[status(thm)],[c_672]) ).
cnf(c_80,plain,
difference(difference(A,B),difference(B,difference(C,difference(A,B)))) = difference(A,B),
inference(paramod,[status(thm)],[c_12,c_1]) ).
cnf(c_102,plain,
difference(difference(A,B),difference(C,difference(A,difference(A,B)))) = difference(difference(A,C),difference(A,difference(A,B))),
inference(paramod,[status(thm)],[c_46,c_4]) ).
cnf(c_673,plain,
difference(difference(A,B),difference(difference(A,B),difference(A,difference(B,difference(C,A))))) = difference(difference(A,B),difference(C,A)),
inference(paramod,[status(thm)],[c_12,c_46]) ).
cnf(c_104,plain,
difference(difference(A,B),difference(difference(A,B),difference(A,difference(B,difference(C,A))))) = difference(A,difference(B,difference(C,A))),
inference(paramod,[status(thm)],[c_12,c_673]) ).
cnf(c_117,plain,
difference(A,difference(difference(B,C),difference(B,difference(C,D)))) = A,
inference(paramod,[status(thm)],[c_48,c_45]) ).
cnf(c_674,plain,
difference(A,B) = difference(A,difference(B,difference(C,A))),
inference(paramod,[status(thm)],[c_117,c_104]) ).
cnf(c_122,plain,
difference(A,difference(B,difference(C,A))) = difference(A,B),
inference(copy,[status(thm)],[c_674]) ).
cnf(c_675,plain,
difference(difference(A,B),C) = difference(difference(A,C),difference(A,difference(A,B))),
inference(paramod,[status(thm)],[c_122,c_102]) ).
cnf(c_124,plain,
difference(difference(A,B),difference(A,difference(A,C))) = difference(difference(A,C),B),
inference(copy,[status(thm)],[c_675]) ).
cnf(c_131,plain,
difference(difference(A,B),difference(B,C)) = difference(A,B),
inference(paramod,[status(thm)],[c_122,c_80]) ).
cnf(c_132,plain,
difference(difference(A,B),difference(C,A)) = difference(A,B),
inference(paramod,[status(thm)],[c_122,c_12]) ).
cnf(c_676,plain,
difference(A,difference(difference(B,A),C)) = difference(A,difference(B,A)),
inference(paramod,[status(thm)],[c_1,c_131]) ).
cnf(c_136,plain,
difference(A,difference(difference(B,A),C)) = A,
inference(paramod,[status(thm)],[c_1,c_676]) ).
cnf(c_677,plain,
difference(difference(difference(A,B),C),B) = difference(difference(A,B),C),
inference(paramod,[status(thm)],[c_1,c_132]) ).
cnf(c_143,plain,
difference(difference(A,B),C) = difference(difference(A,C),B),
inference(paramod,[status(thm)],[c_20,c_677]) ).
cnf(c_164,plain,
difference(A,difference(B,difference(B,difference(C,A)))) = A,
inference(paramod,[status(thm)],[c_2,c_136]) ).
cnf(c_678,plain,
difference(difference(A,B),difference(difference(C,B),difference(D,B))) = difference(difference(A,difference(C,difference(D,B))),difference(B,difference(D,B))),
inference(paramod,[status(thm)],[c_1,c_18]) ).
cnf(c_679,plain,
difference(difference(A,B),difference(difference(C,D),B)) = difference(difference(A,difference(C,difference(D,B))),difference(B,difference(D,B))),
inference(paramod,[status(thm)],[c_4,c_678]) ).
cnf(c_680,plain,
difference(difference(A,difference(C,D)),B) = difference(difference(A,difference(C,difference(D,B))),difference(B,difference(D,B))),
inference(paramod,[status(thm)],[c_4,c_679]) ).
cnf(c_681,plain,
difference(difference(A,difference(C,D)),B) = difference(difference(A,difference(C,difference(D,B))),B),
inference(paramod,[status(thm)],[c_1,c_680]) ).
cnf(c_682,plain,
difference(difference(A,difference(C,D)),B) = difference(difference(A,B),difference(C,difference(D,B))),
inference(paramod,[status(thm)],[c_143,c_681]) ).
cnf(c_224,plain,
difference(difference(A,B),difference(C,difference(D,B))) = difference(difference(A,difference(C,D)),B),
inference(copy,[status(thm)],[c_682]) ).
cnf(c_683,plain,
difference(difference(A,difference(A,difference(B,C))),C) = difference(A,difference(A,difference(B,C))),
inference(paramod,[status(thm)],[c_164,c_1]) ).
cnf(c_684,plain,
difference(difference(A,C),difference(A,difference(B,C))) = difference(A,difference(A,difference(B,C))),
inference(paramod,[status(thm)],[c_143,c_683]) ).
cnf(c_337,plain,
difference(difference(A,difference(A,B)),C) = difference(A,difference(A,difference(B,C))),
inference(paramod,[status(thm)],[c_224,c_684]) ).
cnf(c_685,plain,
difference(difference(A,B),difference(A,difference(C,difference(C,A)))) = difference(difference(A,difference(A,C)),B),
inference(paramod,[status(thm)],[c_2,c_124]) ).
cnf(c_686,plain,
difference(difference(A,B),difference(A,C)) = difference(difference(A,difference(A,C)),B),
inference(paramod,[status(thm)],[c_122,c_685]) ).
cnf(c_391,plain,
difference(difference(A,B),difference(A,C)) = difference(A,difference(A,difference(C,B))),
inference(paramod,[status(thm)],[c_337,c_686]) ).
cnf(c_687,plain,
difference(difference(A,difference(A,B)),difference(A,difference(A,difference(B,C)))) = difference(C,difference(C,difference(A,difference(A,B)))),
inference(paramod,[status(thm)],[c_337,c_2]) ).
cnf(c_688,plain,
difference(A,difference(A,difference(difference(A,difference(B,C)),difference(A,B)))) = difference(C,difference(C,difference(A,difference(A,B)))),
inference(paramod,[status(thm)],[c_391,c_687]) ).
cnf(c_689,plain,
difference(A,difference(A,difference(A,difference(A,difference(B,difference(B,C)))))) = difference(C,difference(C,difference(A,difference(A,B)))),
inference(paramod,[status(thm)],[c_391,c_688]) ).
cnf(c_651,plain,
difference(A,difference(A,difference(B,difference(B,C)))) = difference(C,difference(C,difference(A,difference(A,B)))),
inference(paramod,[status(thm)],[c_46,c_689]) ).
cnf(c_690,plain,
difference(a,difference(a,difference(b,difference(b,c)))) != difference(c,difference(c,difference(a,difference(a,b)))),
inference(copy,[status(thm)],[c_7]) ).
cnf(c_652,plain,
$false,
inference(resolve,[status(thm)],[c_651,c_690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG005-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n026.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 21:00:10 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 1937274 was started by sandbox on n026,
% 0.07/0.35 % Sat Sep 26 21:00:10 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 2.62/1.21
% 2.62/1.21 % SZS status Unsatisfiable for theBenchmark
% 2.62/1.21
% 2.62/1.21 % Proof 1 at 0.28 (+ 0.12) seconds.
% 2.62/1.21 % Length of proof is 36.
% 2.62/1.21 % Level of proof is 16.
% 2.62/1.21 % Maximum clause weight is 69.000.
% 2.62/1.21 % Given clauses 63.
% 2.62/1.21
% 2.62/1.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------