%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET005-1 : 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 : n013.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 0.89s 0.56s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 16 unt; 0 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 101 ( 44 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 51 ( 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(member_of_both_is_member_of_intersection,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_2)
| ~ member(VAR_3,VAR_0)
| ~ member(VAR_3,VAR_1)
| ~ intersection(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_both_is_member_of_intersection) ).
cnf(c_8,plain,
( member(D,C)
| ~ member(D,A)
| ~ member(D,B)
| ~ intersection(A,B,C) ),
inference(clausify,[status(thm)],[member_of_both_is_member_of_intersection]) ).
fof(member_of_intersection_is_member_of_set2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_1)
| ~ member(VAR_3,VAR_2)
| ~ intersection(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_intersection_is_member_of_set2) ).
cnf(c_9,plain,
( member(D,B)
| ~ member(D,C)
| ~ intersection(A,B,C) ),
inference(clausify,[status(thm)],[member_of_intersection_is_member_of_set2]) ).
fof(member_of_intersection_is_member_of_set1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_3,VAR_0)
| ~ member(VAR_3,VAR_2)
| ~ intersection(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',member_of_intersection_is_member_of_set1) ).
cnf(c_10,plain,
( member(D,A)
| ~ member(D,C)
| ~ intersection(A,B,C) ),
inference(clausify,[status(thm)],[member_of_intersection_is_member_of_set1]) ).
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(a_intersection_b,axiom,
intersection(a,b,aIb),
file('theBenchmark.p',a_intersection_b) ).
cnf(c_13,plain,
intersection(a,b,aIb),
inference(clausify,[status(thm)],[a_intersection_b]) ).
fof(b_intersection_c,axiom,
intersection(b,c,bIc),
file('theBenchmark.p',b_intersection_c) ).
cnf(c_14,plain,
intersection(b,c,bIc),
inference(clausify,[status(thm)],[b_intersection_c]) ).
fof(a_intersection_bIc,axiom,
intersection(a,bIc,aIbIc),
file('theBenchmark.p',a_intersection_bIc) ).
cnf(c_15,plain,
intersection(a,bIc,aIbIc),
inference(clausify,[status(thm)],[a_intersection_bIc]) ).
fof(prove_aIb_intersection_c_is_aIbIc,axiom,
~ intersection(aIb,c,aIbIc),
file('theBenchmark.p',prove_aIb_intersection_c_is_aIbIc) ).
cnf(c_16,plain,
~ intersection(aIb,c,aIbIc),
inference(clausify,[status(thm)],[prove_aIb_intersection_c_is_aIbIc]) ).
cnf(c_17,plain,
( member(h(aIb,c,aIbIc),aIb)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(resolve,[status(thm)],[c_16,c_7]) ).
cnf(c_18,plain,
( member(h(aIb,c,aIbIc),c)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(resolve,[status(thm)],[c_16,c_11]) ).
cnf(c_19,plain,
( ~ member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),c)
| ~ member(h(aIb,c,aIbIc),aIbIc) ),
inference(resolve,[status(thm)],[c_16,c_12]) ).
cnf(c_20,plain,
( member(A,a)
| ~ member(A,aIbIc) ),
inference(resolve,[status(thm)],[c_15,c_10]) ).
cnf(c_21,plain,
( member(A,bIc)
| ~ member(A,aIbIc) ),
inference(resolve,[status(thm)],[c_15,c_9]) ).
cnf(c_22,plain,
( member(A,aIbIc)
| ~ member(A,a)
| ~ member(A,bIc) ),
inference(resolve,[status(thm)],[c_15,c_8]) ).
cnf(c_23,plain,
( member(A,b)
| ~ member(A,bIc) ),
inference(resolve,[status(thm)],[c_14,c_10]) ).
cnf(c_24,plain,
( member(A,c)
| ~ member(A,bIc) ),
inference(resolve,[status(thm)],[c_14,c_9]) ).
cnf(c_25,plain,
( member(A,bIc)
| ~ member(A,b)
| ~ member(A,c) ),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_26,plain,
( member(A,a)
| ~ member(A,aIb) ),
inference(resolve,[status(thm)],[c_13,c_10]) ).
cnf(c_27,plain,
( member(A,b)
| ~ member(A,aIb) ),
inference(resolve,[status(thm)],[c_13,c_9]) ).
cnf(c_28,plain,
( member(A,aIb)
| ~ member(A,a)
| ~ member(A,b) ),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_47,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| member(h(aIb,c,aIbIc),bIc)
| ~ member(h(aIb,c,aIbIc),b) ),
inference(resolve,[status(thm)],[c_25,c_18]) ).
cnf(c_48,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| member(h(aIb,c,aIbIc),a) ),
inference(resolve,[status(thm)],[c_26,c_17]) ).
cnf(c_49,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| member(h(aIb,c,aIbIc),b) ),
inference(resolve,[status(thm)],[c_27,c_17]) ).
cnf(c_1118,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| ~ member(h(aIb,c,aIbIc),bIc)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(resolve,[status(thm)],[c_48,c_22]) ).
cnf(c_252,plain,
( ~ member(h(aIb,c,aIbIc),bIc)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(copy,[status(thm)],[c_1118]) ).
cnf(c_1119,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| member(h(aIb,c,aIbIc),bIc)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(resolve,[status(thm)],[c_49,c_47]) ).
cnf(c_392,plain,
( member(h(aIb,c,aIbIc),bIc)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(copy,[status(thm)],[c_1119]) ).
cnf(c_1120,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(resolve,[status(thm)],[c_392,c_252]) ).
cnf(c_846,plain,
member(h(aIb,c,aIbIc),aIbIc),
inference(copy,[status(thm)],[c_1120]) ).
cnf(c_851,plain,
( ~ member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),c) ),
inference(resolve,[status(thm)],[c_846,c_19]) ).
cnf(c_873,plain,
member(h(aIb,c,aIbIc),bIc),
inference(resolve,[status(thm)],[c_846,c_21]) ).
cnf(c_874,plain,
member(h(aIb,c,aIbIc),a),
inference(resolve,[status(thm)],[c_846,c_20]) ).
cnf(c_900,plain,
member(h(aIb,c,aIbIc),c),
inference(resolve,[status(thm)],[c_873,c_24]) ).
cnf(c_901,plain,
member(h(aIb,c,aIbIc),b),
inference(resolve,[status(thm)],[c_873,c_23]) ).
cnf(c_902,plain,
~ member(h(aIb,c,aIbIc),aIb),
inference(resolve,[status(thm)],[c_900,c_851]) ).
cnf(c_1121,plain,
( member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),b) ),
inference(resolve,[status(thm)],[c_874,c_28]) ).
cnf(c_1122,plain,
member(h(aIb,c,aIbIc),aIb),
inference(resolve,[status(thm)],[c_901,c_1121]) ).
cnf(c_1117,plain,
$false,
inference(resolve,[status(thm)],[c_902,c_1122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 06:47:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2144084 was started by sandbox on n013,
% 0.08/0.35 % Sat Sep 26 06:47:06 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.89/0.56
% 0.89/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.89/0.56
% 0.89/0.56 % Proof 1 at 0.13 (+ 0.03) seconds.
% 0.89/0.56 % Length of proof is 35.
% 0.89/0.56 % Level of proof is 8.
% 0.89/0.56 % Maximum clause weight is 28.000.
% 0.89/0.56 % Given clauses 81.
% 0.89/0.56
% 0.89/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------