%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG006-1 : 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 : n003.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 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 46 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 113 ( 13 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,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(prove_set_difference_3_simplified,axiom,
difference(difference(a,c),b) != difference(difference(a,b),c),
file('theBenchmark.p',prove_set_difference_3_simplified) ).
cnf(c_5,plain,
difference(difference(a,c),b) != difference(difference(a,b),c),
inference(clausify,[status(thm)],[prove_set_difference_3_simplified]) ).
cnf(c_6,plain,
difference(difference(A,B),B) = difference(A,B),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_141,plain,
difference(A,A) = difference(difference(B,A),difference(difference(B,A),A)),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_142,plain,
difference(A,A) = difference(difference(B,A),difference(B,A)),
inference(paramod,[status(thm)],[c_6,c_141]) ).
cnf(c_143,plain,
difference(A,A) = difference(difference(B,B),A),
inference(paramod,[status(thm)],[c_4,c_142]) ).
cnf(c_8,plain,
difference(difference(A,A),B) = difference(B,B),
inference(copy,[status(thm)],[c_143]) ).
cnf(c_144,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_10,plain,
difference(difference(A,B),difference(C,A)) = difference(A,difference(B,difference(C,A))),
inference(copy,[status(thm)],[c_144]) ).
cnf(c_145,plain,
difference(difference(A,B),difference(C,B)) = difference(difference(difference(A,B),C),B),
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_146,plain,
difference(difference(A,C),B) = difference(difference(difference(A,B),C),B),
inference(paramod,[status(thm)],[c_4,c_145]) ).
cnf(c_18,plain,
difference(difference(difference(A,B),C),B) = difference(difference(A,C),B),
inference(copy,[status(thm)],[c_146]) ).
cnf(c_147,plain,
difference(difference(A,difference(B,B)),difference(A,difference(B,B))) = difference(B,B),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_19,plain,
difference(difference(A,A),difference(B,B)) = difference(B,B),
inference(paramod,[status(thm)],[c_4,c_147]) ).
cnf(c_148,plain,
difference(difference(A,A),difference(B,B)) = difference(difference(B,B),difference(difference(B,B),difference(A,A))),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_149,plain,
difference(B,B) = difference(difference(B,B),difference(difference(B,B),difference(A,A))),
inference(paramod,[status(thm)],[c_19,c_148]) ).
cnf(c_150,plain,
difference(B,B) = difference(difference(B,B),difference(A,A)),
inference(paramod,[status(thm)],[c_19,c_149]) ).
cnf(c_28,plain,
difference(A,A) = difference(B,B),
inference(paramod,[status(thm)],[c_19,c_150]) ).
cnf(c_31,plain,
difference(A,difference(B,B)) = A,
inference(paramod,[status(thm)],[c_28,c_1]) ).
cnf(c_151,plain,
difference(A,A) = difference(difference(B,B),C),
inference(paramod,[status(thm)],[c_28,c_4]) ).
cnf(c_33,plain,
difference(difference(A,A),B) = difference(C,C),
inference(copy,[status(thm)],[c_151]) ).
cnf(c_152,plain,
difference(A,A) = difference(difference(B,C),B),
inference(paramod,[status(thm)],[c_33,c_4]) ).
cnf(c_36,plain,
difference(difference(A,B),A) = difference(C,C),
inference(copy,[status(thm)],[c_152]) ).
cnf(c_41,plain,
difference(A,difference(difference(B,C),B)) = A,
inference(paramod,[status(thm)],[c_36,c_1]) ).
cnf(c_153,plain,
difference(difference(A,B),difference(C,C)) = difference(A,difference(A,difference(A,B))),
inference(paramod,[status(thm)],[c_36,c_2]) ).
cnf(c_154,plain,
difference(A,B) = difference(A,difference(A,difference(A,B))),
inference(paramod,[status(thm)],[c_31,c_153]) ).
cnf(c_42,plain,
difference(A,difference(A,difference(A,B))) = difference(A,B),
inference(copy,[status(thm)],[c_154]) ).
cnf(c_155,plain,
difference(difference(A,B),difference(C,C)) = difference(difference(A,difference(B,D)),B),
inference(paramod,[status(thm)],[c_36,c_4]) ).
cnf(c_156,plain,
difference(A,B) = difference(difference(A,difference(B,D)),B),
inference(paramod,[status(thm)],[c_31,c_155]) ).
cnf(c_44,plain,
difference(difference(A,difference(B,C)),B) = difference(A,B),
inference(copy,[status(thm)],[c_156]) ).
cnf(c_157,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_10,c_42]) ).
cnf(c_100,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_10,c_157]) ).
cnf(c_113,plain,
difference(A,difference(difference(B,C),difference(B,difference(C,D)))) = A,
inference(paramod,[status(thm)],[c_44,c_41]) ).
cnf(c_158,plain,
difference(A,B) = difference(A,difference(B,difference(C,A))),
inference(paramod,[status(thm)],[c_113,c_100]) ).
cnf(c_118,plain,
difference(A,difference(B,difference(C,A))) = difference(A,B),
inference(copy,[status(thm)],[c_158]) ).
cnf(c_128,plain,
difference(difference(A,B),difference(C,A)) = difference(A,B),
inference(paramod,[status(thm)],[c_118,c_10]) ).
cnf(c_159,plain,
difference(difference(difference(A,B),C),B) = difference(difference(A,B),C),
inference(paramod,[status(thm)],[c_1,c_128]) ).
cnf(c_139,plain,
difference(difference(A,B),C) = difference(difference(A,C),B),
inference(paramod,[status(thm)],[c_18,c_159]) ).
cnf(c_140,plain,
$false,
inference(resolve,[status(thm)],[c_139,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG006-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n003.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sat Sep 26 20:59:09 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 3755949 was started by sandbox on n003,
% 0.20/0.46 % Sat Sep 26 20:59:09 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.47
% 0.20/0.47 % From the command line: assign(max_seconds, 300).
% 0.20/0.52
% 0.20/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.52
% 0.20/0.52 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.20/0.52 % Length of proof is 23.
% 0.20/0.52 % Level of proof is 12.
% 0.20/0.52 % Maximum clause weight is 69.000.
% 0.20/0.52 % Given clauses 23.
% 0.20/0.52
% 0.20/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------