%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET578+3 : 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 : n017.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 08:36:30 AM UTC 2026
% Result : Theorem 1.27s 0.82s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 180 ( 50 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 177 ( 46 ~; 103 |; 21 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 88 ( 2 sgn 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersection_defn) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(prove_th19,conjecture,
! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,D)
& member(E,C) ) )
=> B = intersection(C,D) ),
file('theBenchmark.p',prove_th19) ).
fof(prove_th19_neg,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,D)
& member(E,C) ) )
=> B = intersection(C,D) ),
inference(assume_negation,[status(cth)],[prove_th19]) ).
cnf(c_8,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_9,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_10,plain,
( ~ member(A,C)
| ~ member(A,B)
| member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_14,plain,
intersection(A,B) = intersection(B,A),
inference(clausify,[status(thm)],[commutativity_of_intersection]) ).
fof(nnf_6,plain,
! [B,C] :
( ( ? [D] :
( ( ~ member(D,C)
| ~ member(D,B) )
& ( member(D,C)
| member(D,B) ) )
| C = B )
& ( ! [X0] :
( ( ~ member(X0,C)
| member(X0,B) )
& ( member(X0,C)
| ~ member(X0,B) ) )
| C != B ) ),
inference(fof_nnf,[status(thm)],[equal_member_defn]) ).
fof(sk_equal_member_defn_sk,plain,
! [B,C] :
( ( ( ( ~ member(sK0(B,C),C)
| ~ member(sK0(B,C),B) )
& ( member(sK0(B,C),C)
| member(sK0(B,C),B) ) )
| C = B )
& ( ! [X0] :
( ( ~ member(X0,C)
| member(X0,B) )
& ( member(X0,C)
| ~ member(X0,B) ) )
| C != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(B,C))],[nnf_6]) ).
fof(sk_equal_member_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK0(VAR_1,VAR_0),VAR_0)
| ~ member(sK0(VAR_1,VAR_0),VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1] :
( member(sK0(VAR_1,VAR_0),VAR_0)
| member(sK0(VAR_1,VAR_0),VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_2,VAR_0)
| member(VAR_2,VAR_1)
| VAR_0 != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_0)
| ~ member(VAR_2,VAR_1)
| VAR_0 != VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_equal_member_defn_sk]) ).
cnf(c_21,plain,
( member(sK0(B,A),A)
| member(sK0(B,A),B)
| A = B ),
inference(split_conjunct,[status(thm)],[sk_equal_member_defn]) ).
cnf(c_22,plain,
( ~ member(sK0(B,A),A)
| ~ member(sK0(B,A),B)
| A = B ),
inference(split_conjunct,[status(thm)],[sk_equal_member_defn]) ).
fof(nnf_7,plain,
? [B,C,D] :
( intersection(C,D) != B
& ! [E] :
( ( ~ member(E,D)
| ~ member(E,C)
| member(E,B) )
& ( ( member(E,D)
& member(E,C) )
| ~ member(E,B) ) ) ),
inference(fof_nnf,[status(thm)],[prove_th19_neg]) ).
fof(sk_prove_th19_neg_sk,plain,
( intersection(sK2,sK3) != sK1
& ! [E] :
( ( ~ member(E,sK3)
| ~ member(E,sK2)
| member(E,sK1) )
& ( ( member(E,sK3)
& member(E,sK2) )
| ~ member(E,sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_7]) ).
fof(sk_prove_th19_neg,plain,
( intersection(sK2,sK3) != sK1
& ! [VAR_0] :
( ~ member(VAR_0,sK3)
| ~ member(VAR_0,sK2)
| member(VAR_0,sK1) )
& ! [VAR_0] :
( member(VAR_0,sK3)
| ~ member(VAR_0,sK1) )
& ! [VAR_0] :
( member(VAR_0,sK2)
| ~ member(VAR_0,sK1) ) ),
inference(cnf_transformation,[status(thm)],[sk_prove_th19_neg_sk]) ).
cnf(c_23,negated_conjecture,
( member(A,sK2)
| ~ member(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_prove_th19_neg]) ).
cnf(c_24,negated_conjecture,
( member(A,sK3)
| ~ member(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_prove_th19_neg]) ).
cnf(c_25,negated_conjecture,
( ~ member(A,sK3)
| ~ member(A,sK2)
| member(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_prove_th19_neg]) ).
cnf(c_26,negated_conjecture,
intersection(sK2,sK3) != sK1,
inference(split_conjunct,[status(thm)],[sk_prove_th19_neg]) ).
cnf(c_659,plain,
( member(sK0(intersection(B,C),A),C)
| member(sK0(intersection(B,C),A),A)
| A = intersection(B,C) ),
inference(resolve,[status(thm)],[c_21,c_9]) ).
cnf(c_37,plain,
( member(sK0(intersection(A,B),C),B)
| member(sK0(intersection(A,B),C),C)
| intersection(A,B) = C ),
inference(copy,[status(thm)],[c_659]) ).
cnf(c_660,plain,
( member(sK0(intersection(B,C),A),B)
| member(sK0(intersection(B,C),A),A)
| A = intersection(B,C) ),
inference(resolve,[status(thm)],[c_21,c_8]) ).
cnf(c_38,plain,
( member(sK0(intersection(A,B),C),A)
| member(sK0(intersection(A,B),C),C)
| intersection(A,B) = C ),
inference(copy,[status(thm)],[c_660]) ).
cnf(c_65,plain,
( member(sK0(A,sK1),A)
| sK1 = A
| member(sK0(A,sK1),sK2) ),
inference(resolve,[status(thm)],[c_23,c_21]) ).
cnf(c_69,plain,
( member(sK0(A,sK1),A)
| sK1 = A
| member(sK0(A,sK1),sK3) ),
inference(resolve,[status(thm)],[c_24,c_21]) ).
cnf(c_661,plain,
( member(sK0(A,sK1),A)
| sK1 = A
| ~ member(sK0(A,sK1),B)
| member(sK0(A,sK1),intersection(sK2,B)) ),
inference(resolve,[status(thm)],[c_10,c_65]) ).
cnf(c_662,plain,
( member(sK0(A,sK1),A)
| sK1 = A
| member(sK0(A,sK1),A)
| sK1 = A
| member(sK0(A,sK1),intersection(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_661,c_69]) ).
cnf(c_663,plain,
( member(sK0(A,sK1),A)
| member(sK0(A,sK1),A)
| sK1 = A
| member(sK0(A,sK1),intersection(sK2,sK3)) ),
inference(copy,[status(thm)],[c_662]) ).
cnf(c_294,plain,
( member(sK0(A,sK1),A)
| sK1 = A
| member(sK0(A,sK1),intersection(sK2,sK3)) ),
inference(copy,[status(thm)],[c_663]) ).
cnf(c_664,plain,
( sK1 = intersection(sK2,sK3)
| member(sK0(intersection(sK2,sK3),sK1),intersection(sK2,sK3)) ),
inference(factor,[status(thm)],[c_294]) ).
cnf(c_665,plain,
( intersection(sK2,sK3) = sK1
| member(sK0(intersection(sK2,sK3),sK1),intersection(sK2,sK3)) ),
inference(copy,[status(thm)],[c_664]) ).
cnf(c_306,negated_conjecture,
member(sK0(intersection(sK2,sK3),sK1),intersection(sK2,sK3)),
inference(resolve,[status(thm)],[c_26,c_665]) ).
cnf(c_666,negated_conjecture,
( member(sK0(intersection(A,sK2),B),B)
| intersection(A,sK2) = B
| ~ member(sK0(intersection(A,sK2),B),sK3)
| member(sK0(intersection(A,sK2),B),sK1) ),
inference(resolve,[status(thm)],[c_25,c_37]) ).
cnf(c_667,negated_conjecture,
( member(sK0(intersection(sK3,sK2),A),A)
| intersection(sK3,sK2) = A
| member(sK0(intersection(sK3,sK2),A),A)
| intersection(sK3,sK2) = A
| member(sK0(intersection(sK3,sK2),A),sK1) ),
inference(resolve,[status(thm)],[c_666,c_38]) ).
cnf(c_668,negated_conjecture,
( member(sK0(intersection(sK3,sK2),A),A)
| intersection(sK3,sK2) = A
| member(sK0(intersection(sK3,sK2),A),A)
| intersection(sK3,sK2) = A
| member(sK0(intersection(sK2,sK3),A),sK1) ),
inference(paramod,[status(thm)],[c_14,c_667]) ).
cnf(c_669,negated_conjecture,
( member(sK0(intersection(sK3,sK2),A),A)
| intersection(sK3,sK2) = A
| member(sK0(intersection(sK3,sK2),A),A)
| intersection(sK2,sK3) = A
| member(sK0(intersection(sK2,sK3),A),sK1) ),
inference(paramod,[status(thm)],[c_14,c_668]) ).
cnf(c_670,negated_conjecture,
( member(sK0(intersection(sK3,sK2),A),A)
| intersection(sK3,sK2) = A
| member(sK0(intersection(sK2,sK3),A),A)
| intersection(sK2,sK3) = A
| member(sK0(intersection(sK2,sK3),A),sK1) ),
inference(paramod,[status(thm)],[c_14,c_669]) ).
cnf(c_671,negated_conjecture,
( member(sK0(intersection(sK3,sK2),A),A)
| intersection(sK2,sK3) = A
| member(sK0(intersection(sK2,sK3),A),A)
| intersection(sK2,sK3) = A
| member(sK0(intersection(sK2,sK3),A),sK1) ),
inference(paramod,[status(thm)],[c_14,c_670]) ).
cnf(c_672,negated_conjecture,
( member(sK0(intersection(sK2,sK3),A),A)
| intersection(sK2,sK3) = A
| member(sK0(intersection(sK2,sK3),A),A)
| intersection(sK2,sK3) = A
| member(sK0(intersection(sK2,sK3),A),sK1) ),
inference(paramod,[status(thm)],[c_14,c_671]) ).
cnf(c_673,negated_conjecture,
( member(sK0(intersection(sK2,sK3),A),A)
| member(sK0(intersection(sK2,sK3),A),A)
| intersection(sK2,sK3) = A
| member(sK0(intersection(sK2,sK3),A),sK1) ),
inference(copy,[status(thm)],[c_672]) ).
cnf(c_607,negated_conjecture,
( member(sK0(intersection(sK2,sK3),A),A)
| intersection(sK2,sK3) = A
| member(sK0(intersection(sK2,sK3),A),sK1) ),
inference(copy,[status(thm)],[c_673]) ).
cnf(c_674,plain,
( intersection(sK2,sK3) = sK1
| member(sK0(intersection(sK2,sK3),sK1),sK1) ),
inference(factor,[status(thm)],[c_607]) ).
cnf(c_653,negated_conjecture,
member(sK0(intersection(sK2,sK3),sK1),sK1),
inference(resolve,[status(thm)],[c_26,c_674]) ).
cnf(c_675,plain,
( ~ member(sK0(intersection(sK2,sK3),sK1),intersection(sK2,sK3))
| sK1 = intersection(sK2,sK3) ),
inference(resolve,[status(thm)],[c_653,c_22]) ).
cnf(c_676,plain,
( ~ member(sK0(intersection(sK2,sK3),sK1),intersection(sK2,sK3))
| intersection(sK2,sK3) = sK1 ),
inference(copy,[status(thm)],[c_675]) ).
cnf(c_677,negated_conjecture,
~ member(sK0(intersection(sK2,sK3),sK1),intersection(sK2,sK3)),
inference(resolve,[status(thm)],[c_26,c_676]) ).
cnf(c_658,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_306,c_677]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET578+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 07:52:18 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.39 % Process 208936 was started by sandbox on n017,
% 0.10/0.39 % Sat Sep 26 07:52:18 2026
% 0.10/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 1.27/0.82
% 1.27/0.82 % SZS status Theorem for theBenchmark
% 1.27/0.82
% 1.27/0.82 % Proof 1 at 0.12 (+ 0.04) seconds.
% 1.27/0.82 % Length of proof is 23.
% 1.27/0.82 % Level of proof is 5.
% 1.27/0.82 % Maximum clause weight is 34.000.
% 1.27/0.82 % Given clauses 85.
% 1.27/0.82
% 1.27/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------