%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET628+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 : n026.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 08:36:40 AM UTC 2026
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 6 unt; 0 def)
% Number of atoms : 117 ( 27 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 129 ( 50 ~; 55 |; 18 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 3 sgn 39 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(equal_member_defn,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('theBenchmark.p',equal_member_defn) ).
fof(not_equal_defn,axiom,
! [B,C] :
( not_equal(B,C)
<=> B != C ),
file('theBenchmark.p',not_equal_defn) ).
fof(prove_th110,conjecture,
! [B] :
( intersect(B,B)
<=> not_equal(B,empty_set) ),
file('theBenchmark.p',prove_th110) ).
fof(prove_th110_neg,negated_conjecture,
~ ! [B] :
( intersect(B,B)
<=> not_equal(B,empty_set) ),
inference(assume_negation,[status(cth)],[prove_th110]) ).
fof(nnf_7,plain,
? [B] :
( ( ~ not_equal(B,empty_set)
| ~ intersect(B,B) )
& ( not_equal(B,empty_set)
| intersect(B,B) ) ),
inference(fof_nnf,[status(thm)],[prove_th110_neg]) ).
fof(sk_prove_th110_neg,plain,
( ( ~ not_equal(sK0,empty_set)
| ~ intersect(sK0,sK0) )
& ( not_equal(sK0,empty_set)
| intersect(sK0,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_7]) ).
cnf(c_11,negated_conjecture,
( ~ not_equal(sK0,empty_set)
| ~ intersect(sK0,sK0) ),
inference(split_conjunct,[status(thm)],[sk_prove_th110_neg]) ).
cnf(c_12,negated_conjecture,
( not_equal(sK0,empty_set)
| intersect(sK0,sK0) ),
inference(split_conjunct,[status(thm)],[sk_prove_th110_neg]) ).
cnf(c_14,plain,
( B = A
| not_equal(A,B) ),
inference(clausify,[status(thm)],[not_equal_defn]) ).
cnf(c_15,plain,
( B != A
| ~ not_equal(A,B) ),
inference(clausify,[status(thm)],[not_equal_defn]) ).
fof(nnf_3,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(sK1(B,C),C)
| ~ member(sK1(B,C),B) )
& ( member(sK1(B,C),C)
| member(sK1(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,[sK1]),skolemize(D,sK1(B,C))],[nnf_3]) ).
fof(sk_equal_member_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK1(VAR_1,VAR_0),VAR_0)
| ~ member(sK1(VAR_1,VAR_0),VAR_1)
| VAR_0 = VAR_1 )
& ! [VAR_0,VAR_1] :
( member(sK1(VAR_1,VAR_0),VAR_0)
| member(sK1(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_17,plain,
( member(sK1(B,A),A)
| member(sK1(B,A),B)
| A = B ),
inference(split_conjunct,[status(thm)],[sk_equal_member_defn]) ).
cnf(c_20,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set_defn]) ).
fof(nnf_1,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [X0] :
( member(X0,C)
& member(X0,B) )
| ~ intersect(B,C) ) ),
inference(fof_nnf,[status(thm)],[intersect_defn]) ).
fof(sk_intersect_defn_sk,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ( member(sK2(B,C),C)
& member(sK2(B,C),B) )
| ~ intersect(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2(B,C))],[nnf_1]) ).
fof(sk_intersect_defn,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| intersect(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK2(VAR_0,VAR_1),VAR_1)
| ~ intersect(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK2(VAR_0,VAR_1),VAR_0)
| ~ intersect(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_intersect_defn_sk]) ).
cnf(c_21,plain,
( ~ member(C,B)
| ~ member(C,A)
| intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_22,plain,
( member(sK2(A,B),B)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_24,plain,
( ~ member(B,A)
| intersect(A,A) ),
inference(factor,[status(thm)],[c_21]) ).
cnf(c_55,negated_conjecture,
( ~ intersect(sK0,sK0)
| empty_set = sK0 ),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_25,negated_conjecture,
( ~ intersect(sK0,sK0)
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_56,negated_conjecture,
( intersect(sK0,sK0)
| empty_set != sK0 ),
inference(resolve,[status(thm)],[c_15,c_12]) ).
cnf(c_26,negated_conjecture,
( intersect(sK0,sK0)
| sK0 != empty_set ),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_36,plain,
( member(sK1(A,empty_set),A)
| empty_set = A ),
inference(resolve,[status(thm)],[c_20,c_17]) ).
cnf(c_42,plain,
~ intersect(A,empty_set),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_46,plain,
( intersect(A,A)
| empty_set = A ),
inference(resolve,[status(thm)],[c_36,c_24]) ).
cnf(c_57,plain,
( sK0 = empty_set
| empty_set = sK0 ),
inference(resolve,[status(thm)],[c_46,c_25]) ).
cnf(c_58,plain,
( sK0 = empty_set
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_52,plain,
sK0 = empty_set,
inference(copy,[status(thm)],[c_58]) ).
cnf(c_59,negated_conjecture,
( intersect(sK0,sK0)
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_52,c_26]) ).
cnf(c_60,negated_conjecture,
( intersect(empty_set,sK0)
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_52,c_59]) ).
cnf(c_61,negated_conjecture,
( intersect(empty_set,empty_set)
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_52,c_60]) ).
cnf(c_62,negated_conjecture,
intersect(empty_set,empty_set),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_54,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_42,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET628+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n026.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 08:04:26 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 488366 was started by sandbox on n026,
% 0.09/0.35 % Sat Sep 26 08:04:26 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.13/0.36
% 0.13/0.36 % SZS status Theorem for theBenchmark
% 0.13/0.36
% 0.13/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.36 % Length of proof is 21.
% 0.13/0.36 % Level of proof is 5.
% 0.13/0.36 % Maximum clause weight is 13.000.
% 0.13/0.36 % Given clauses 22.
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------