%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU154+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 08:45:12 AM UTC 2026
% Result : Theorem 16.88s 12.81s
% Output : CNFRefutation 16.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 26 unt; 0 def)
% Number of atoms : 195 ( 44 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 206 ( 82 ~; 88 |; 25 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 146 ( 7 sgn 67 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(t2_xboole_1,axiom,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(l28_zfmisc_1,conjecture,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('theBenchmark.p',l28_zfmisc_1) ).
fof(l28_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
inference(assume_negation,[status(cth)],[l28_zfmisc_1]) ).
cnf(c_18,plain,
( ~ in(B,A)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_19,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_21,plain,
( subset(A,B)
| A != B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
cnf(c_23,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_24,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
fof(nnf_5,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_5]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_27,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_28,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
fof(nnf_6,plain,
! [A,B,C] :
( ( ? [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| in(D,C) ) )
| set_intersection2(A,B) = C )
& ( ! [X0] :
( ( ~ in(X0,B)
| ~ in(X0,A)
| in(X0,C) )
& ( ( in(X0,B)
& in(X0,A) )
| ~ in(X0,C) ) )
| set_intersection2(A,B) != C ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(sk_d3_xboole_0_sk,plain,
! [A,B,C] :
( ( ( ( ~ in(sK1(A,B,C),B)
| ~ in(sK1(A,B,C),A)
| ~ in(sK1(A,B,C),C) )
& ( ( in(sK1(A,B,C),B)
& in(sK1(A,B,C),A) )
| in(sK1(A,B,C),C) ) )
| set_intersection2(A,B) = C )
& ( ! [X0] :
( ( ~ in(X0,B)
| ~ in(X0,A)
| in(X0,C) )
& ( ( in(X0,B)
& in(X0,A) )
| ~ in(X0,C) ) )
| set_intersection2(A,B) != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(D,sK1(A,B,C))],[nnf_6]) ).
fof(sk_d3_xboole_0,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(sK1(VAR_0,VAR_1,VAR_2),VAR_1)
| ~ in(sK1(VAR_0,VAR_1,VAR_2),VAR_0)
| ~ in(sK1(VAR_0,VAR_1,VAR_2),VAR_2)
| set_intersection2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK1(VAR_0,VAR_1,VAR_2),VAR_1)
| in(sK1(VAR_0,VAR_1,VAR_2),VAR_2)
| set_intersection2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK1(VAR_0,VAR_1,VAR_2),VAR_0)
| in(sK1(VAR_0,VAR_1,VAR_2),VAR_2)
| set_intersection2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(VAR_3,VAR_1)
| ~ in(VAR_3,VAR_0)
| in(VAR_3,VAR_2)
| set_intersection2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(VAR_3,VAR_1)
| ~ in(VAR_3,VAR_2)
| set_intersection2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(VAR_3,VAR_0)
| ~ in(VAR_3,VAR_2)
| set_intersection2(VAR_0,VAR_1) != VAR_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_xboole_0_sk]) ).
cnf(c_31,plain,
( in(D,B)
| ~ in(D,C)
| set_intersection2(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_d3_xboole_0]) ).
cnf(c_32,plain,
( ~ in(D,B)
| ~ in(D,A)
| in(D,C)
| set_intersection2(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_d3_xboole_0]) ).
cnf(c_33,plain,
( in(sK1(A,B,C),A)
| in(sK1(A,B,C),C)
| set_intersection2(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d3_xboole_0]) ).
cnf(c_34,plain,
( in(sK1(A,B,C),B)
| in(sK1(A,B,C),C)
| set_intersection2(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d3_xboole_0]) ).
cnf(c_37,plain,
( set_intersection2(A,B) != empty_set
| disjoint(A,B) ),
inference(clausify,[status(thm)],[d7_xboole_0]) ).
cnf(c_39,plain,
set_intersection2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k3_xboole_0]) ).
cnf(c_44,plain,
subset(empty_set,A),
inference(clausify,[status(thm)],[t2_xboole_1]) ).
fof(nnf_17,plain,
? [A,B] :
( ~ disjoint(singleton(A),B)
& ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1_neg]) ).
fof(sk_l28_zfmisc_1_neg,plain,
( ~ disjoint(singleton(sK2),sK3)
& ~ in(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(A,sK2),skolemize(B,sK3)],[nnf_17]) ).
cnf(c_45,negated_conjecture,
~ in(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_l28_zfmisc_1_neg]) ).
cnf(c_46,negated_conjecture,
~ disjoint(singleton(sK2),sK3),
inference(split_conjunct,[status(thm)],[sk_l28_zfmisc_1_neg]) ).
cnf(c_47,plain,
~ in(A,A),
inference(factor,[status(thm)],[c_18]) ).
cnf(c_56,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_23]) ).
cnf(c_57,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_24]) ).
cnf(c_63,plain,
( in(C,B)
| ~ in(C,A)
| in(sK0(A,B),A) ),
inference(resolve,[status(thm)],[c_28,c_27]) ).
cnf(c_70,plain,
( ~ in(A,B)
| ~ in(A,C)
| in(A,set_intersection2(B,C)) ),
inference(resolve,[status(thm)],[c_32,c_19]) ).
cnf(c_84,plain,
( in(sK1(A,B,C),D)
| ~ subset(A,D)
| in(sK1(A,B,C),C)
| set_intersection2(A,B) = C ),
inference(resolve,[status(thm)],[c_33,c_27]) ).
cnf(c_5928,plain,
A = set_intersection2(A,A),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_5929,plain,
( in(A,C)
| ~ in(A,set_intersection2(set_intersection2(B,C),set_intersection2(B,C))) ),
inference(resolve,[status(thm)],[c_31,c_5928]) ).
cnf(c_5930,negated_conjecture,
~ in(sK2,set_intersection2(set_intersection2(A,sK3),set_intersection2(A,sK3))),
inference(resolve,[status(thm)],[c_5929,c_45]) ).
cnf(c_128,negated_conjecture,
~ in(sK2,set_intersection2(A,sK3)),
inference(paramod,[status(thm)],[c_39,c_5930]) ).
cnf(c_5931,negated_conjecture,
set_intersection2(singleton(sK2),sK3) != empty_set,
inference(resolve,[status(thm)],[c_37,c_46]) ).
cnf(c_132,negated_conjecture,
set_intersection2(sK3,singleton(sK2)) != empty_set,
inference(paramod,[status(thm)],[c_19,c_5931]) ).
cnf(c_5932,plain,
( in(A,B)
| ~ in(A,empty_set) ),
inference(resolve,[status(thm)],[c_27,c_44]) ).
cnf(c_135,plain,
~ in(A,empty_set),
inference(resolve,[status(thm)],[c_5932,c_47]) ).
cnf(c_5933,plain,
in(set_intersection2(A,A),singleton(A)),
inference(resolve,[status(thm)],[c_57,c_39]) ).
cnf(c_174,plain,
in(A,singleton(A)),
inference(paramod,[status(thm)],[c_39,c_5933]) ).
cnf(c_253,plain,
( in(sK1(C,D,A),D)
| set_intersection2(C,D) = A
| in(sK1(C,D,A),B)
| in(sK0(A,B),A) ),
inference(resolve,[status(thm)],[c_63,c_34]) ).
cnf(c_255,plain,
( in(sK1(C,D,A),C)
| set_intersection2(C,D) = A
| in(sK1(C,D,A),B)
| in(sK0(A,B),A) ),
inference(resolve,[status(thm)],[c_63,c_33]) ).
cnf(c_5934,plain,
( in(sK1(sK3,singleton(sK2),empty_set),A)
| ~ subset(sK3,A)
| in(sK1(sK3,singleton(sK2),empty_set),empty_set) ),
inference(resolve,[status(thm)],[c_84,c_132]) ).
cnf(c_5935,plain,
( in(sK1(sK3,singleton(sK2),empty_set),A)
| ~ subset(sK3,A) ),
inference(resolve,[status(thm)],[c_5934,c_135]) ).
cnf(c_646,plain,
~ subset(sK3,sK1(sK3,singleton(sK2),empty_set)),
inference(resolve,[status(thm)],[c_5935,c_47]) ).
cnf(c_5936,plain,
sK3 != sK1(sK3,singleton(sK2),empty_set),
inference(resolve,[status(thm)],[c_21,c_646]) ).
cnf(c_989,plain,
sK1(sK3,singleton(sK2),empty_set) != sK3,
inference(copy,[status(thm)],[c_5936]) ).
cnf(c_1141,plain,
~ in(sK1(sK3,singleton(sK2),empty_set),singleton(sK3)),
inference(resolve,[status(thm)],[c_56,c_989]) ).
cnf(c_5937,plain,
( in(sK1(sK3,singleton(sK2),empty_set),singleton(sK2))
| set_intersection2(sK3,singleton(sK2)) = empty_set
| in(sK0(empty_set,singleton(sK3)),empty_set) ),
inference(resolve,[status(thm)],[c_253,c_1141]) ).
cnf(c_5938,plain,
( in(sK1(sK3,singleton(sK2),empty_set),singleton(sK2))
| set_intersection2(sK3,singleton(sK2)) = empty_set ),
inference(resolve,[status(thm)],[c_135,c_5937]) ).
cnf(c_5086,plain,
in(sK1(sK3,singleton(sK2),empty_set),singleton(sK2)),
inference(resolve,[status(thm)],[c_132,c_5938]) ).
cnf(c_5939,plain,
( in(sK1(sK3,singleton(sK2),empty_set),sK3)
| set_intersection2(sK3,singleton(sK2)) = empty_set
| in(sK0(empty_set,singleton(sK3)),empty_set) ),
inference(resolve,[status(thm)],[c_255,c_1141]) ).
cnf(c_5940,plain,
( in(sK1(sK3,singleton(sK2),empty_set),sK3)
| set_intersection2(sK3,singleton(sK2)) = empty_set ),
inference(resolve,[status(thm)],[c_135,c_5939]) ).
cnf(c_5534,plain,
in(sK1(sK3,singleton(sK2),empty_set),sK3),
inference(resolve,[status(thm)],[c_132,c_5940]) ).
cnf(c_5747,plain,
( ~ in(sK1(sK3,singleton(sK2),empty_set),A)
| in(sK1(sK3,singleton(sK2),empty_set),set_intersection2(A,sK3)) ),
inference(resolve,[status(thm)],[c_5534,c_70]) ).
cnf(c_5913,plain,
sK1(sK3,singleton(sK2),empty_set) = sK2,
inference(resolve,[status(thm)],[c_5086,c_56]) ).
cnf(c_5941,plain,
( ~ in(sK1(sK3,singleton(sK2),empty_set),A)
| in(sK2,set_intersection2(A,sK3)) ),
inference(paramod,[status(thm)],[c_5913,c_5747]) ).
cnf(c_5942,plain,
( ~ in(sK2,A)
| in(sK2,set_intersection2(A,sK3)) ),
inference(paramod,[status(thm)],[c_5913,c_5941]) ).
cnf(c_5926,plain,
~ in(sK2,A),
inference(resolve,[status(thm)],[c_128,c_5942]) ).
cnf(c_5927,plain,
$false,
inference(resolve,[status(thm)],[c_5926,c_174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU154+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n004.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Sat Sep 26 08:41:18 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.38 % Process 1271441 was started by sandbox on n004,
% 0.09/10.38 % Sat Sep 26 08:41:18 2026
% 0.09/10.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/10.38
% 0.09/10.38 % From the command line: assign(max_seconds, 300).
% 16.88/12.81
% 16.88/12.81 % given #500 (T,wt=24): 238 empty_set != A | set_intersection2(B,C) = A | in(f3(B,C,A),C). [resolve(233,b,34,b)].
% 16.88/12.81
% 16.88/12.81 % SZS status Theorem for theBenchmark
% 16.88/12.81
% 16.88/12.81 % Proof 1 at 1.90 (+ 0.51) seconds.
% 16.88/12.81 % Length of proof is 47.
% 16.88/12.81 % Level of proof is 10.
% 16.88/12.81 % Maximum clause weight is 32.000.
% 16.88/12.81 % Given clauses 606.
% 16.88/12.81
% 16.88/12.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------