%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU131+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 : n020.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 08:45:06 AM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 9 unt; 0 def)
% Number of atoms : 150 ( 37 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 171 ( 63 ~; 78 |; 24 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 91 ( 3 sgn 54 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
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(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(l32_xboole_1,conjecture,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',l32_xboole_1) ).
fof(l32_xboole_1_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
inference(assume_negation,[status(cth)],[l32_xboole_1]) ).
fof(nnf_2,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_2]) ).
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_17,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_18,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_19,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
fof(nnf_3,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_3]) ).
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_21,plain,
( ~ in(D,B)
| ~ in(D,C)
| set_difference(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_d4_xboole_0]) ).
cnf(c_22,plain,
( in(D,B)
| ~ in(D,A)
| in(D,C)
| set_difference(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_d4_xboole_0]) ).
cnf(c_23,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_24,plain,
( ~ in(sK1(A,B,C),B)
| in(sK1(A,B,C),C)
| set_difference(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d4_xboole_0]) ).
cnf(c_32,plain,
set_difference(A,empty_set) = A,
inference(clausify,[status(thm)],[t3_boole]) ).
fof(nnf_15,plain,
? [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) != empty_set )
& ( subset(A,B)
| set_difference(A,B) = empty_set ) ),
inference(fof_nnf,[status(thm)],[l32_xboole_1_neg]) ).
fof(sk_l32_xboole_1_neg,plain,
( ( ~ subset(sK2,sK3)
| set_difference(sK2,sK3) != empty_set )
& ( subset(sK2,sK3)
| set_difference(sK2,sK3) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(A,sK2),skolemize(B,sK3)],[nnf_15]) ).
cnf(c_37,negated_conjecture,
( subset(sK2,sK3)
| set_difference(sK2,sK3) = empty_set ),
inference(split_conjunct,[status(thm)],[sk_l32_xboole_1_neg]) ).
cnf(c_38,negated_conjecture,
( ~ subset(sK2,sK3)
| set_difference(sK2,sK3) != empty_set ),
inference(split_conjunct,[status(thm)],[sk_l32_xboole_1_neg]) ).
cnf(c_58,plain,
( in(sK1(A,B,C),D)
| ~ subset(A,D)
| in(sK1(A,B,C),C)
| set_difference(A,B) = C ),
inference(resolve,[status(thm)],[c_23,c_17]) ).
cnf(c_97,plain,
( ~ in(A,empty_set)
| ~ in(A,B) ),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_100,plain,
~ in(A,empty_set),
inference(factor,[status(thm)],[c_97]) ).
cnf(c_109,plain,
( in(sK0(sK2,sK3),sK2)
| set_difference(sK2,sK3) != empty_set ),
inference(resolve,[status(thm)],[c_38,c_18]) ).
cnf(c_265,plain,
( set_difference(sK2,sK3) = empty_set
| in(sK1(sK2,A,B),sK3)
| in(sK1(sK2,A,B),B)
| set_difference(sK2,A) = B ),
inference(resolve,[status(thm)],[c_58,c_37]) ).
cnf(c_338,plain,
( in(sK1(sK2,sK3,empty_set),sK3)
| in(sK1(sK2,sK3,empty_set),empty_set)
| set_difference(sK2,sK3) = empty_set ),
inference(factor,[status(thm)],[c_265]) ).
cnf(c_266,plain,
( in(sK1(sK2,sK3,empty_set),sK3)
| set_difference(sK2,sK3) = empty_set ),
inference(resolve,[status(thm)],[c_100,c_338]) ).
cnf(c_339,plain,
( in(sK1(sK2,sK3,empty_set),empty_set)
| set_difference(sK2,sK3) = empty_set
| set_difference(sK2,sK3) = empty_set ),
inference(resolve,[status(thm)],[c_266,c_24]) ).
cnf(c_340,plain,
( in(sK1(sK2,sK3,empty_set),empty_set)
| set_difference(sK2,sK3) = empty_set ),
inference(copy,[status(thm)],[c_339]) ).
cnf(c_321,plain,
set_difference(sK2,sK3) = empty_set,
inference(resolve,[status(thm)],[c_100,c_340]) ).
cnf(c_341,plain,
( in(sK0(sK2,sK3),sK2)
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_321,c_109]) ).
cnf(c_322,plain,
in(sK0(sK2,sK3),sK2),
inference(copy,[status(thm)],[c_341]) ).
cnf(c_342,negated_conjecture,
( ~ subset(sK2,sK3)
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_321,c_38]) ).
cnf(c_323,negated_conjecture,
~ subset(sK2,sK3),
inference(copy,[status(thm)],[c_342]) ).
cnf(c_324,negated_conjecture,
~ in(sK0(sK2,sK3),sK3),
inference(resolve,[status(thm)],[c_19,c_323]) ).
cnf(c_343,plain,
( in(A,sK3)
| ~ in(A,sK2)
| in(A,empty_set) ),
inference(resolve,[status(thm)],[c_22,c_321]) ).
cnf(c_344,plain,
( in(A,sK3)
| ~ in(A,sK2) ),
inference(resolve,[status(thm)],[c_343,c_100]) ).
cnf(c_345,plain,
~ in(sK0(sK2,sK3),sK2),
inference(resolve,[status(thm)],[c_344,c_324]) ).
cnf(c_337,plain,
$false,
inference(resolve,[status(thm)],[c_322,c_345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU131+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 08:39:05 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 1108273 was started by sandbox2 on n020,
% 0.11/0.38 % Sat Sep 26 08:39:05 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 0.11/0.44
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44
% 0.11/0.44 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.11/0.44 % Length of proof is 25.
% 0.11/0.44 % Level of proof is 8.
% 0.11/0.44 % Maximum clause weight is 32.000.
% 0.11/0.44 % Given clauses 118.
% 0.11/0.44
% 0.11/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------