%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU141+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 08:45:08 AM UTC 2026
% Result : Theorem 20.77s 8.04s
% Output : CNFRefutation 20.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 14 unt; 0 def)
% Number of atoms : 211 ( 42 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 234 ( 92 ~; 100 |; 32 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 145 ( 9 sgn 78 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t4_xboole_0,axiom,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t83_xboole_1,conjecture,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t83_xboole_1_neg,negated_conjecture,
~ ! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
inference(assume_negation,[status(cth)],[t83_xboole_1]) ).
cnf(c_25,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_28,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
fof(nnf_4,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_4]) ).
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_30,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_32,plain,
( in(D,A)
| ~ in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
cnf(c_34,plain,
( ~ in(D,B)
| ~ in(D,A)
| in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
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_difference(A,B) = C )
& ( ! [X0] :
( ( in(X0,B)
| ~ in(X0,A)
| in(X0,C) )
& ( ( ~ in(X0,B)
& in(X0,A) )
| ~ in(X0,C) ) )
| set_difference(A,B) != C ) ),
inference(fof_nnf,[status(thm)],[d4_xboole_0]) ).
fof(sk_d4_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_difference(A,B) = C )
& ( ! [X0] :
( ( in(X0,B)
| ~ in(X0,A)
| in(X0,C) )
& ( ( ~ in(X0,B)
& in(X0,A) )
| ~ in(X0,C) ) )
| set_difference(A,B) != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(D,sK1(A,B,C))],[nnf_6]) ).
fof(sk_d4_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_difference(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_difference(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_difference(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_difference(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_difference(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_difference(VAR_0,VAR_1) != VAR_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_d4_xboole_0_sk]) ).
cnf(c_39,plain,
( ~ in(D,B)
| ~ in(D,C)
| set_difference(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_d4_xboole_0]) ).
cnf(c_41,plain,
( in(sK1(A,B,C),A)
| in(sK1(A,B,C),C)
| set_difference(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d4_xboole_0]) ).
cnf(c_43,plain,
( in(sK1(A,B,C),B)
| ~ in(sK1(A,B,C),A)
| ~ in(sK1(A,B,C),C)
| set_difference(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d4_xboole_0]) ).
cnf(c_51,plain,
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[symmetry_r1_xboole_0]) ).
cnf(c_53,plain,
set_difference(A,empty_set) = A,
inference(clausify,[status(thm)],[t3_boole]) ).
fof(nnf_19,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [X0] : in(X0,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t4_xboole_0]) ).
fof(sk_t4_xboole_0_sk,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( in(sK2(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2(A,B))],[nnf_19]) ).
fof(sk_t4_xboole_0,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ disjoint(VAR_1,VAR_2)
| ~ in(VAR_0,set_intersection2(VAR_1,VAR_2)) )
& ! [VAR_0,VAR_1] :
( in(sK2(VAR_0,VAR_1),set_intersection2(VAR_0,VAR_1))
| disjoint(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_t4_xboole_0_sk]) ).
cnf(c_55,plain,
( in(sK2(A,B),set_intersection2(A,B))
| disjoint(A,B) ),
inference(split_conjunct,[status(thm)],[sk_t4_xboole_0]) ).
cnf(c_56,plain,
( ~ disjoint(B,C)
| ~ in(A,set_intersection2(B,C)) ),
inference(split_conjunct,[status(thm)],[sk_t4_xboole_0]) ).
fof(nnf_23,plain,
? [A,B] :
( ( set_difference(A,B) != A
| ~ disjoint(A,B) )
& ( set_difference(A,B) = A
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t83_xboole_1_neg]) ).
fof(sk_t83_xboole_1_neg,plain,
( ( set_difference(sK3,sK4) != sK3
| ~ disjoint(sK3,sK4) )
& ( set_difference(sK3,sK4) = sK3
| disjoint(sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(A,sK3),skolemize(B,sK4)],[nnf_23]) ).
cnf(c_60,negated_conjecture,
( set_difference(sK3,sK4) = sK3
| disjoint(sK3,sK4) ),
inference(split_conjunct,[status(thm)],[sk_t83_xboole_1_neg]) ).
cnf(c_61,negated_conjecture,
( set_difference(sK3,sK4) != sK3
| ~ disjoint(sK3,sK4) ),
inference(split_conjunct,[status(thm)],[sk_t83_xboole_1_neg]) ).
cnf(c_75,plain,
( ~ subset(B,A)
| A = B
| in(sK0(A,B),A) ),
inference(resolve,[status(thm)],[c_30,c_28]) ).
cnf(c_79,plain,
( in(A,C)
| ~ in(A,set_intersection2(B,C)) ),
inference(resolve,[status(thm)],[c_32,c_25]) ).
cnf(c_80,plain,
( in(A,B)
| ~ in(A,set_intersection2(B,C)) ),
inference(xxres,[status(thm)],[c_32]) ).
cnf(c_261,plain,
( ~ in(A,empty_set)
| ~ in(A,B) ),
inference(resolve,[status(thm)],[c_53,c_39]) ).
cnf(c_266,plain,
~ in(A,empty_set),
inference(factor,[status(thm)],[c_261]) ).
cnf(c_318,plain,
( ~ disjoint(C,B)
| ~ in(A,set_intersection2(B,C)) ),
inference(paramod,[status(thm)],[c_25,c_56]) ).
cnf(c_334,plain,
( disjoint(sK4,sK3)
| set_difference(sK3,sK4) = sK3 ),
inference(resolve,[status(thm)],[c_60,c_51]) ).
cnf(c_372,plain,
( in(sK2(sK3,sK4),set_intersection2(sK3,sK4))
| set_difference(sK3,sK4) != sK3 ),
inference(resolve,[status(thm)],[c_61,c_55]) ).
cnf(c_9194,negated_conjecture,
( in(sK1(sK3,sK4,sK3),sK3)
| in(sK1(sK3,sK4,sK3),sK3)
| ~ disjoint(sK3,sK4) ),
inference(resolve,[status(thm)],[c_61,c_41]) ).
cnf(c_373,negated_conjecture,
( in(sK1(sK3,sK4,sK3),sK3)
| ~ disjoint(sK3,sK4) ),
inference(copy,[status(thm)],[c_9194]) ).
cnf(c_547,plain,
subset(empty_set,A),
inference(resolve,[status(thm)],[c_266,c_30]) ).
cnf(c_9195,plain,
( A = empty_set
| in(sK0(A,empty_set),A) ),
inference(resolve,[status(thm)],[c_75,c_547]) ).
cnf(c_593,plain,
( empty_set = A
| in(sK0(A,empty_set),A) ),
inference(copy,[status(thm)],[c_9195]) ).
cnf(c_777,plain,
( disjoint(A,B)
| in(sK2(A,B),B) ),
inference(resolve,[status(thm)],[c_79,c_55]) ).
cnf(c_790,plain,
( disjoint(A,B)
| in(sK2(A,B),A) ),
inference(resolve,[status(thm)],[c_80,c_55]) ).
cnf(c_924,plain,
( ~ in(A,sK4)
| ~ in(A,sK3)
| disjoint(sK4,sK3) ),
inference(resolve,[status(thm)],[c_334,c_39]) ).
cnf(c_9196,plain,
( ~ disjoint(B,A)
| empty_set = set_intersection2(A,B) ),
inference(resolve,[status(thm)],[c_593,c_318]) ).
cnf(c_1273,plain,
( ~ disjoint(B,A)
| set_intersection2(A,B) = empty_set ),
inference(copy,[status(thm)],[c_9196]) ).
cnf(c_3720,plain,
( ~ in(sK2(A,sK3),sK4)
| disjoint(sK4,sK3)
| disjoint(A,sK3) ),
inference(resolve,[status(thm)],[c_777,c_924]) ).
cnf(c_3766,plain,
( ~ in(sK2(sK4,sK3),sK4)
| disjoint(sK4,sK3) ),
inference(factor,[status(thm)],[c_3720]) ).
cnf(c_9197,plain,
( disjoint(sK4,sK3)
| disjoint(sK4,sK3) ),
inference(resolve,[status(thm)],[c_3766,c_790]) ).
cnf(c_8084,plain,
disjoint(sK4,sK3),
inference(copy,[status(thm)],[c_9197]) ).
cnf(c_8087,plain,
set_intersection2(sK3,sK4) = empty_set,
inference(resolve,[status(thm)],[c_8084,c_1273]) ).
cnf(c_8088,plain,
disjoint(sK3,sK4),
inference(resolve,[status(thm)],[c_8084,c_51]) ).
cnf(c_9198,plain,
( in(sK2(sK3,sK4),empty_set)
| set_difference(sK3,sK4) != sK3 ),
inference(paramod,[status(thm)],[c_8087,c_372]) ).
cnf(c_8097,plain,
set_difference(sK3,sK4) != sK3,
inference(resolve,[status(thm)],[c_266,c_9198]) ).
cnf(c_8129,negated_conjecture,
in(sK1(sK3,sK4,sK3),sK3),
inference(resolve,[status(thm)],[c_8088,c_373]) ).
cnf(c_9199,plain,
( ~ in(A,sK4)
| ~ in(A,sK3)
| in(A,empty_set) ),
inference(resolve,[status(thm)],[c_8087,c_34]) ).
cnf(c_8158,plain,
( ~ in(A,sK4)
| ~ in(A,sK3) ),
inference(resolve,[status(thm)],[c_266,c_9199]) ).
cnf(c_9172,plain,
~ in(sK1(sK3,sK4,sK3),sK4),
inference(resolve,[status(thm)],[c_8129,c_8158]) ).
cnf(c_9200,plain,
( in(sK1(sK3,sK4,sK3),sK4)
| ~ in(sK1(sK3,sK4,sK3),sK3)
| set_difference(sK3,sK4) = sK3 ),
inference(resolve,[status(thm)],[c_8129,c_43]) ).
cnf(c_9201,plain,
( in(sK1(sK3,sK4,sK3),sK4)
| ~ in(sK1(sK3,sK4,sK3),sK3) ),
inference(resolve,[status(thm)],[c_8097,c_9200]) ).
cnf(c_9202,plain,
in(sK1(sK3,sK4,sK3),sK4),
inference(resolve,[status(thm)],[c_8129,c_9201]) ).
cnf(c_9193,plain,
$false,
inference(resolve,[status(thm)],[c_9172,c_9202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU141+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n015.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sat Sep 26 08:43:19 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.37 % Process 3607328 was started by sandbox2 on n015,
% 0.08/5.37 % Sat Sep 26 08:43:19 2026
% 0.08/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.39
% 0.08/5.39 % From the command line: assign(max_seconds, 300).
% 20.77/8.04
% 20.77/8.04 % SZS status Theorem for theBenchmark
% 20.77/8.04
% 20.77/8.04 % Proof 1 at 1.90 (+ 0.70) seconds.
% 20.77/8.04 % Length of proof is 48.
% 20.77/8.04 % Level of proof is 10.
% 20.77/8.04 % Maximum clause weight is 27.000.
% 20.77/8.04 % Given clauses 300.
% 20.77/8.04
% 20.77/8.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------