%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET011-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 08:35:16 AM UTC 2026
% Result : Unsatisfiable 9.84s 1.76s
% Output : CNFRefutation 9.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 12 unt; 0 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 86 ( 38 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 47 ( 2 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_axiom1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(h(VAR_0,VAR_1,VAR_2),VAR_0)
| intersection(VAR_0,VAR_1,VAR_2)
| member(h(VAR_0,VAR_1,VAR_2),VAR_2) ),
file('theBenchmark.p',intersection_axiom1) ).
cnf(c_7,plain,
( member(h(A,B,C),A)
| intersection(A,B,C)
| member(h(A,B,C),C) ),
inference(clausify,[status(thm)],[intersection_axiom1]) ).
fof(intersection_axiom2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(h(VAR_0,VAR_1,VAR_2),VAR_1)
| intersection(VAR_0,VAR_1,VAR_2)
| member(h(VAR_0,VAR_1,VAR_2),VAR_2) ),
file('theBenchmark.p',intersection_axiom2) ).
cnf(c_11,plain,
( member(h(A,B,C),B)
| intersection(A,B,C)
| member(h(A,B,C),C) ),
inference(clausify,[status(thm)],[intersection_axiom2]) ).
fof(intersection_axiom3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( intersection(VAR_0,VAR_1,VAR_2)
| ~ member(h(VAR_0,VAR_1,VAR_2),VAR_0)
| ~ member(h(VAR_0,VAR_1,VAR_2),VAR_1)
| ~ member(h(VAR_0,VAR_1,VAR_2),VAR_2) ),
file('theBenchmark.p',intersection_axiom3) ).
cnf(c_12,plain,
( intersection(A,B,C)
| ~ member(h(A,B,C),A)
| ~ member(h(A,B,C),B)
| ~ member(h(A,B,C),C) ),
inference(clausify,[status(thm)],[intersection_axiom3]) ).
fof(prove_a_intersection_b_is_aD_aDb,axiom,
~ intersection(a,b,aD_aDb),
file('theBenchmark.p',prove_a_intersection_b_is_aD_aDb) ).
cnf(c_13,plain,
~ intersection(a,b,aD_aDb),
inference(clausify,[status(thm)],[prove_a_intersection_b_is_aD_aDb]) ).
fof(member_of_difference_or_set2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_0,VAR_2)
| member(VAR_0,VAR_3)
| ~ difference(VAR_1,VAR_2,VAR_3)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',member_of_difference_or_set2) ).
cnf(c_14,plain,
( member(A,C)
| member(A,D)
| ~ difference(B,C,D)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[member_of_difference_or_set2]) ).
fof(a_minus_b,axiom,
difference(a,b,aDb),
file('theBenchmark.p',a_minus_b) ).
cnf(c_18,plain,
difference(a,b,aDb),
inference(clausify,[status(thm)],[a_minus_b]) ).
fof(a_minus_aDb,axiom,
difference(a,aDb,aD_aDb),
file('theBenchmark.p',a_minus_aDb) ).
cnf(c_19,plain,
difference(a,aDb,aD_aDb),
inference(clausify,[status(thm)],[a_minus_aDb]) ).
fof(not_member_of_difference,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ difference(VAR_3,VAR_1,VAR_2)
| ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',not_member_of_difference) ).
cnf(c_20,plain,
( ~ difference(D,B,C)
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[not_member_of_difference]) ).
fof(member_of_difference,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_0)
| ~ member(VAR_3,VAR_2)
| ~ difference(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_difference) ).
cnf(c_21,plain,
( member(D,A)
| ~ member(D,C)
| ~ difference(A,B,C) ),
inference(clausify,[status(thm)],[member_of_difference]) ).
cnf(c_22,plain,
( member(A,a)
| ~ member(A,aD_aDb) ),
inference(resolve,[status(thm)],[c_21,c_19]) ).
cnf(c_27,plain,
( ~ member(A,aD_aDb)
| ~ member(A,aDb) ),
inference(resolve,[status(thm)],[c_20,c_19]) ).
cnf(c_28,plain,
( ~ member(A,aDb)
| ~ member(A,b) ),
inference(resolve,[status(thm)],[c_20,c_18]) ).
cnf(c_32,plain,
( member(A,aDb)
| member(A,aD_aDb)
| ~ member(A,a) ),
inference(resolve,[status(thm)],[c_14,c_19]) ).
cnf(c_33,plain,
( member(A,b)
| member(A,aDb)
| ~ member(A,a) ),
inference(resolve,[status(thm)],[c_14,c_18]) ).
cnf(c_48,plain,
( ~ member(h(a,b,aD_aDb),a)
| ~ member(h(a,b,aD_aDb),b)
| ~ member(h(a,b,aD_aDb),aD_aDb) ),
inference(resolve,[status(thm)],[c_13,c_12]) ).
cnf(c_49,plain,
( member(h(a,b,aD_aDb),b)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(resolve,[status(thm)],[c_13,c_11]) ).
cnf(c_50,plain,
( member(h(a,b,aD_aDb),a)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(resolve,[status(thm)],[c_13,c_7]) ).
cnf(c_73,plain,
( ~ member(h(a,b,aD_aDb),aDb)
| member(h(a,b,aD_aDb),b) ),
inference(resolve,[status(thm)],[c_49,c_27]) ).
cnf(c_87,plain,
( ~ member(h(a,b,aD_aDb),aDb)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(resolve,[status(thm)],[c_49,c_28]) ).
cnf(c_4515,plain,
( member(h(a,b,aD_aDb),a)
| member(h(a,b,aD_aDb),a) ),
inference(resolve,[status(thm)],[c_50,c_22]) ).
cnf(c_130,plain,
member(h(a,b,aD_aDb),a),
inference(copy,[status(thm)],[c_4515]) ).
cnf(c_4516,plain,
( member(h(a,b,aD_aDb),aDb)
| member(h(a,b,aD_aDb),aD_aDb)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(resolve,[status(thm)],[c_50,c_32]) ).
cnf(c_137,plain,
( member(h(a,b,aD_aDb),aDb)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(copy,[status(thm)],[c_4516]) ).
cnf(c_144,plain,
( ~ member(h(a,b,aD_aDb),b)
| ~ member(h(a,b,aD_aDb),aD_aDb) ),
inference(resolve,[status(thm)],[c_130,c_48]) ).
cnf(c_259,plain,
( member(h(a,b,aD_aDb),b)
| member(h(a,b,aD_aDb),aDb) ),
inference(resolve,[status(thm)],[c_130,c_33]) ).
cnf(c_4517,plain,
( member(h(a,b,aD_aDb),aD_aDb)
| member(h(a,b,aD_aDb),aD_aDb) ),
inference(resolve,[status(thm)],[c_137,c_87]) ).
cnf(c_4109,plain,
member(h(a,b,aD_aDb),aD_aDb),
inference(copy,[status(thm)],[c_4517]) ).
cnf(c_4135,plain,
~ member(h(a,b,aD_aDb),b),
inference(resolve,[status(thm)],[c_4109,c_144]) ).
cnf(c_4469,plain,
member(h(a,b,aD_aDb),aDb),
inference(resolve,[status(thm)],[c_4135,c_259]) ).
cnf(c_4518,plain,
~ member(h(a,b,aD_aDb),aDb),
inference(resolve,[status(thm)],[c_4135,c_73]) ).
cnf(c_4514,plain,
$false,
inference(resolve,[status(thm)],[c_4469,c_4518]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n007.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 06:46:40 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 3030856 was started by sandbox on n007,
% 0.18/0.46 % Sat Sep 26 06:46:40 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 9.84/1.76
% 9.84/1.76 % SZS status Unsatisfiable for theBenchmark
% 9.84/1.76
% 9.84/1.76 % Proof 1 at 0.78 (+ 0.32) seconds.
% 9.84/1.76 % Length of proof is 27.
% 9.84/1.76 % Level of proof is 6.
% 9.84/1.76 % Maximum clause weight is 22.000.
% 9.84/1.76 % Given clauses 218.
% 9.84/1.76
% 9.84/1.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------