%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG007-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 0.23s 10.92s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 61 ( 61 unt; 0 def)
% Number of atoms : 61 ( 60 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 139 ( 6 sgn 7 !; 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_simplified,axiom,
! [VAR_0,VAR_1,VAR_2] : difference(difference(VAR_0,VAR_1),VAR_2) = difference(difference(VAR_0,VAR_2),VAR_1),
file('theBenchmark.p',set_difference_3_simplified) ).
cnf(c_3,plain,
difference(difference(A,B),C) = difference(difference(A,C),B),
inference(clausify,[status(thm)],[set_difference_3_simplified]) ).
fof(prove_set_difference_3,axiom,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
file('theBenchmark.p',prove_set_difference_3) ).
cnf(c_4,plain,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
inference(clausify,[status(thm)],[prove_set_difference_3]) ).
cnf(c_5,plain,
difference(difference(a,c),difference(b,c)) != difference(difference(a,b),c),
inference(copy,[status(thm)],[c_4]) ).
cnf(c_6,plain,
difference(difference(A,B),B) = difference(A,B),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
difference(difference(A,B),difference(B,difference(B,A))) = difference(A,B),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_687,plain,
difference(A,A) = difference(difference(B,A),difference(difference(B,A),A)),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_688,plain,
difference(A,A) = difference(difference(B,A),difference(B,A)),
inference(paramod,[status(thm)],[c_6,c_687]) ).
cnf(c_8,plain,
difference(difference(A,B),difference(A,B)) = difference(B,B),
inference(copy,[status(thm)],[c_688]) ).
cnf(c_689,plain,
difference(A,difference(B,difference(B,A))) = difference(difference(A,B),difference(difference(A,B),A)),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_9,plain,
difference(A,difference(B,difference(B,A))) = difference(A,difference(A,difference(A,B))),
inference(paramod,[status(thm)],[c_2,c_689]) ).
cnf(c_690,plain,
difference(A,B) = difference(difference(A,B),difference(C,A)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_11,plain,
difference(difference(A,B),difference(C,A)) = difference(A,B),
inference(copy,[status(thm)],[c_690]) ).
cnf(c_12,plain,
difference(difference(A,B),difference(difference(A,C),B)) = difference(C,difference(C,difference(A,B))),
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_13,plain,
difference(difference(A,difference(A,B)),C) = difference(difference(B,C),difference(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_691,plain,
difference(difference(A,B),difference(A,B)) = difference(difference(B,difference(B,A)),difference(difference(B,difference(B,A)),difference(A,B))),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_692,plain,
difference(B,B) = difference(difference(B,difference(B,A)),difference(difference(B,difference(B,A)),difference(A,B))),
inference(paramod,[status(thm)],[c_8,c_691]) ).
cnf(c_693,plain,
difference(B,B) = difference(difference(B,difference(B,A)),difference(B,difference(B,A))),
inference(paramod,[status(thm)],[c_11,c_692]) ).
cnf(c_694,plain,
difference(B,B) = difference(difference(B,A),difference(B,A)),
inference(paramod,[status(thm)],[c_8,c_693]) ).
cnf(c_17,plain,
difference(A,A) = difference(B,B),
inference(paramod,[status(thm)],[c_8,c_694]) ).
cnf(c_28,plain,
difference(difference(A,difference(B,difference(B,A))),C) = difference(difference(A,C),difference(A,difference(A,B))),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_695,plain,
difference(A,difference(difference(A,difference(A,B)),difference(difference(A,difference(A,B)),A))) = difference(A,difference(A,difference(A,difference(B,difference(B,A))))),
inference(paramod,[status(thm)],[c_9,c_9]) ).
cnf(c_696,plain,
difference(A,difference(difference(A,difference(A,B)),difference(difference(A,A),difference(A,B)))) = difference(A,difference(A,difference(A,difference(B,difference(B,A))))),
inference(paramod,[status(thm)],[c_3,c_695]) ).
cnf(c_697,plain,
difference(A,difference(A,difference(A,difference(A,difference(A,B))))) = difference(A,difference(A,difference(A,difference(B,difference(B,A))))),
inference(paramod,[status(thm)],[c_12,c_696]) ).
cnf(c_37,plain,
difference(A,difference(A,difference(A,difference(B,difference(B,A))))) = difference(A,difference(A,difference(A,difference(A,difference(A,B))))),
inference(copy,[status(thm)],[c_697]) ).
cnf(c_38,plain,
difference(A,difference(B,B)) = A,
inference(paramod,[status(thm)],[c_17,c_1]) ).
cnf(c_698,plain,
difference(difference(A,A),B) = difference(difference(C,B),C),
inference(paramod,[status(thm)],[c_17,c_3]) ).
cnf(c_39,plain,
difference(difference(A,B),A) = difference(difference(C,C),B),
inference(copy,[status(thm)],[c_698]) ).
cnf(c_41,plain,
difference(difference(A,A),B) = difference(A,A),
inference(paramod,[status(thm)],[c_38,c_1]) ).
cnf(c_42,plain,
difference(difference(A,B),A) = difference(C,C),
inference(paramod,[status(thm)],[c_41,c_39]) ).
cnf(c_699,plain,
difference(difference(A,B),difference(C,C)) = difference(A,difference(A,difference(A,B))),
inference(paramod,[status(thm)],[c_42,c_2]) ).
cnf(c_700,plain,
difference(A,B) = difference(A,difference(A,difference(A,B))),
inference(paramod,[status(thm)],[c_38,c_699]) ).
cnf(c_44,plain,
difference(A,difference(A,difference(A,B))) = difference(A,B),
inference(copy,[status(thm)],[c_700]) ).
cnf(c_701,plain,
difference(A,difference(B,difference(B,A))) = difference(A,difference(A,difference(A,difference(A,difference(A,B))))),
inference(paramod,[status(thm)],[c_44,c_37]) ).
cnf(c_702,plain,
difference(A,difference(B,difference(B,A))) = difference(A,difference(A,difference(A,B))),
inference(paramod,[status(thm)],[c_44,c_701]) ).
cnf(c_52,plain,
difference(A,difference(B,difference(B,A))) = difference(A,B),
inference(paramod,[status(thm)],[c_44,c_702]) ).
cnf(c_703,plain,
difference(difference(A,B),C) = difference(difference(A,C),difference(A,difference(A,B))),
inference(paramod,[status(thm)],[c_52,c_28]) ).
cnf(c_54,plain,
difference(difference(A,B),difference(A,difference(A,C))) = difference(difference(A,C),B),
inference(copy,[status(thm)],[c_703]) ).
cnf(c_58,plain,
difference(difference(difference(A,B),C),difference(D,difference(A,C))) = difference(difference(A,C),B),
inference(paramod,[status(thm)],[c_3,c_11]) ).
cnf(c_704,plain,
difference(difference(A,B),difference(difference(A,difference(A,C)),B)) = difference(difference(A,C),difference(difference(B,difference(B,A)),C)),
inference(paramod,[status(thm)],[c_13,c_12]) ).
cnf(c_705,plain,
difference(difference(A,C),difference(difference(A,C),difference(A,B))) = difference(difference(A,C),difference(difference(B,difference(B,A)),C)),
inference(paramod,[status(thm)],[c_12,c_704]) ).
cnf(c_109,plain,
difference(difference(A,B),difference(difference(C,difference(C,A)),B)) = difference(difference(A,B),difference(difference(A,B),difference(A,C))),
inference(copy,[status(thm)],[c_705]) ).
cnf(c_706,plain,
difference(difference(A,B),difference(difference(A,C),B)) = difference(difference(A,difference(A,C)),difference(difference(A,difference(A,C)),difference(A,B))),
inference(paramod,[status(thm)],[c_44,c_12]) ).
cnf(c_707,plain,
difference(C,difference(C,difference(A,B))) = difference(difference(A,difference(A,C)),difference(difference(A,difference(A,C)),difference(A,B))),
inference(paramod,[status(thm)],[c_12,c_706]) ).
cnf(c_129,plain,
difference(difference(A,difference(A,B)),difference(difference(A,difference(A,B)),difference(A,C))) = difference(B,difference(B,difference(A,C))),
inference(copy,[status(thm)],[c_707]) ).
cnf(c_422,plain,
difference(difference(A,B),difference(A,difference(A,C))) = difference(difference(A,B),C),
inference(paramod,[status(thm)],[c_54,c_3]) ).
cnf(c_708,plain,
difference(difference(difference(A,B),difference(difference(A,B),difference(A,C))),B) = difference(difference(A,B),C),
inference(paramod,[status(thm)],[c_58,c_13]) ).
cnf(c_709,plain,
difference(difference(difference(A,B),B),difference(difference(A,B),difference(A,C))) = difference(difference(A,B),C),
inference(paramod,[status(thm)],[c_3,c_708]) ).
cnf(c_573,plain,
difference(difference(A,B),difference(difference(A,B),difference(A,C))) = difference(difference(A,B),C),
inference(paramod,[status(thm)],[c_6,c_709]) ).
cnf(c_598,plain,
difference(difference(A,difference(A,B)),C) = difference(B,difference(B,difference(A,C))),
inference(paramod,[status(thm)],[c_573,c_129]) ).
cnf(c_710,plain,
difference(difference(A,B),difference(A,difference(A,difference(C,B)))) = difference(difference(A,B),difference(difference(A,B),difference(A,C))),
inference(paramod,[status(thm)],[c_598,c_109]) ).
cnf(c_711,plain,
difference(difference(A,B),difference(C,B)) = difference(difference(A,B),difference(difference(A,B),difference(A,C))),
inference(paramod,[status(thm)],[c_422,c_710]) ).
cnf(c_599,plain,
difference(difference(A,B),difference(C,B)) = difference(difference(A,B),C),
inference(paramod,[status(thm)],[c_573,c_711]) ).
cnf(c_712,plain,
difference(difference(a,c),b) != difference(difference(a,b),c),
inference(paramod,[status(thm)],[c_599,c_5]) ).
cnf(c_713,plain,
difference(difference(a,b),c) != difference(difference(a,b),c),
inference(paramod,[status(thm)],[c_3,c_712]) ).
cnf(c_686,plain,
$false,
inference(copy,[status(thm)],[c_713]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG007-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/10.45 % Computer : n008.cluster.edu
% 0.17/10.45 % Model : x86_64 x86_64
% 0.17/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.45 % Memory : 8046.5625MB
% 0.17/10.45 % OS : Linux 6.8.0-71-generic
% 0.17/10.45 % CPULimit : 300
% 0.17/10.45 % WCLimit : 300
% 0.17/10.45 % DateTime : Sat Sep 26 20:59:07 UTC 2026
% 0.17/10.46 % CPUTime :
% 0.17/10.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/10.46 % Process 349832 was started by sandbox2 on n008,
% 0.17/10.46 % Sat Sep 26 20:59:07 2026
% 0.17/10.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/10.47
% 0.17/10.47 % From the command line: assign(max_seconds, 300).
% 0.23/10.92
% 0.23/10.92 % SZS status Unsatisfiable for theBenchmark
% 0.23/10.92
% 0.23/10.92 % Proof 1 at 0.30 (+ 0.13) seconds.
% 0.23/10.92 % Length of proof is 30.
% 0.23/10.92 % Level of proof is 12.
% 0.23/10.92 % Maximum clause weight is 93.000.
% 0.23/10.92 % Given clauses 42.
% 0.23/10.92
% 0.23/10.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------