%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 08:35:15 AM UTC 2026
% Result : Unsatisfiable 0.05s 5.56s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 13 ~; 15 |; 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 : 23 ( 2 sgn 11 !; 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(a_intersection_bDa,axiom,
~ intersection(a,bDa,aI_bDa),
file('theBenchmark.p',a_intersection_bDa) ).
cnf(c_13,plain,
~ intersection(a,bDa,aI_bDa),
inference(clausify,[status(thm)],[a_intersection_bDa]) ).
fof(b_minus_a,axiom,
difference(b,a,bDa),
file('theBenchmark.p',b_minus_a) ).
cnf(c_18,plain,
difference(b,a,bDa),
inference(clausify,[status(thm)],[b_minus_a]) ).
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_19,plain,
( ~ difference(D,B,C)
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[not_member_of_difference]) ).
cnf(c_25,plain,
( ~ member(A,bDa)
| ~ member(A,a) ),
inference(resolve,[status(thm)],[c_19,c_18]) ).
fof(prove_aI_bDa_is_empty,axiom,
! [VAR_0] : ~ member(VAR_0,aI_bDa),
file('theBenchmark.p',prove_aI_bDa_is_empty) ).
cnf(c_35,plain,
~ member(A,aI_bDa),
inference(clausify,[status(thm)],[prove_aI_bDa_is_empty]) ).
cnf(c_45,plain,
( member(h(a,bDa,aI_bDa),bDa)
| member(h(a,bDa,aI_bDa),aI_bDa) ),
inference(resolve,[status(thm)],[c_13,c_11]) ).
cnf(c_46,plain,
member(h(a,bDa,aI_bDa),bDa),
inference(resolve,[status(thm)],[c_35,c_45]) ).
cnf(c_47,plain,
( member(h(a,bDa,aI_bDa),a)
| member(h(a,bDa,aI_bDa),aI_bDa) ),
inference(resolve,[status(thm)],[c_13,c_7]) ).
cnf(c_48,plain,
member(h(a,bDa,aI_bDa),a),
inference(resolve,[status(thm)],[c_35,c_47]) ).
cnf(c_89,plain,
~ member(h(a,bDa,aI_bDa),a),
inference(resolve,[status(thm)],[c_25,c_46]) ).
cnf(c_88,plain,
$false,
inference(resolve,[status(thm)],[c_48,c_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.05/5.54 % Computer : n012.cluster.edu
% 0.05/5.54 % Model : x86_64 x86_64
% 0.05/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.54 % Memory : 8046.5625MB
% 0.05/5.54 % OS : Linux 6.8.0-71-generic
% 0.05/5.54 % CPULimit : 300
% 0.05/5.54 % WCLimit : 300
% 0.05/5.54 % DateTime : Sat Sep 26 06:48:18 UTC 2026
% 0.05/5.54 % CPUTime :
% 0.05/5.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/5.54 % Process 4117813 was started by sandbox2 on n012,
% 0.05/5.54 % Sat Sep 26 06:48:18 2026
% 0.05/5.54 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.05/5.55
% 0.05/5.55 % From the command line: assign(max_seconds, 300).
% 0.05/5.56
% 0.05/5.56 % SZS status Unsatisfiable for theBenchmark
% 0.05/5.56
% 0.05/5.56 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.05/5.56 % Length of proof is 12.
% 0.05/5.56 % Level of proof is 3.
% 0.05/5.56 % Maximum clause weight is 6.000.
% 0.05/5.56 % Given clauses 25.
% 0.05/5.56
% 0.05/5.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------