%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU203+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 : n001.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 08:45:24 AM UTC 2026
% Result : Theorem 8.28s 2.79s
% Output : CNFRefutation 8.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 11 unt; 0 def)
% Number of atoms : 205 ( 31 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 260 ( 106 ~; 112 |; 32 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 128 ( 6 sgn 55 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d13_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('theBenchmark.p',d13_relat_1) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('theBenchmark.p',d4_relat_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(t143_relat_1,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) ) ) ),
file('theBenchmark.p',t143_relat_1) ).
fof(t143_relat_1_neg,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(A,relation_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) ) ) ),
inference(assume_negation,[status(cth)],[t143_relat_1]) ).
fof(nnf_4,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| ~ in(D,C) )
& ( ? [X3] :
( in(X3,B)
& in(ordered_pair(X3,D),A) )
| in(D,C) ) )
| relation_image(A,B) = C )
& ( ! [X0] :
( ( ! [X2] :
( ~ in(X2,B)
| ~ in(ordered_pair(X2,X0),A) )
| in(X0,C) )
& ( ? [X1] :
( in(X1,B)
& in(ordered_pair(X1,X0),A) )
| ~ in(X0,C) ) )
| relation_image(A,B) != C ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d13_relat_1]) ).
fof(sk_d13_relat_1_sk,plain,
! [A] :
( ! [B,C] :
( ( ( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,sK5(A,B,C)),A) )
| ~ in(sK5(A,B,C),C) )
& ( ( in(sK6(A,B,C),B)
& in(ordered_pair(sK6(A,B,C),sK5(A,B,C)),A) )
| in(sK5(A,B,C),C) ) )
| relation_image(A,B) = C )
& ( ! [X0] :
( ( ! [X2] :
( ~ in(X2,B)
| ~ in(ordered_pair(X2,X0),A) )
| in(X0,C) )
& ( ( in(sK0(A,B,C,X0),B)
& in(ordered_pair(sK0(A,B,C,X0),X0),A) )
| ~ in(X0,C) ) )
| relation_image(A,B) != C ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK5,sK6]),skolemize(X1,sK0(A,B,C,X0)),skolemize(D,sK5(A,B,C)),skolemize(X3,sK6(A,B,C))],[nnf_4]) ).
fof(sk_d13_relat_1,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(VAR_3,VAR_1)
| ~ in(ordered_pair(VAR_3,sK5(VAR_0,VAR_1,VAR_2)),VAR_0)
| ~ in(sK5(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_image(VAR_0,VAR_1) = VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK6(VAR_0,VAR_1,VAR_2),VAR_1)
| in(sK5(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_image(VAR_0,VAR_1) = VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(ordered_pair(sK6(VAR_0,VAR_1,VAR_2),sK5(VAR_0,VAR_1,VAR_2)),VAR_0)
| in(sK5(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_image(VAR_0,VAR_1) = VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ in(VAR_4,VAR_1)
| ~ in(ordered_pair(VAR_4,VAR_3),VAR_0)
| in(VAR_3,VAR_2)
| relation_image(VAR_0,VAR_1) != VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(sK0(VAR_0,VAR_1,VAR_2,VAR_3),VAR_1)
| ~ in(VAR_3,VAR_2)
| relation_image(VAR_0,VAR_1) != VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(ordered_pair(sK0(VAR_0,VAR_1,VAR_2,VAR_3),VAR_3),VAR_0)
| ~ in(VAR_3,VAR_2)
| relation_image(VAR_0,VAR_1) != VAR_2
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d13_relat_1_sk]) ).
cnf(c_31,plain,
( in(ordered_pair(sK0(A,B,C,D),D),A)
| ~ in(D,C)
| relation_image(A,B) != C
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d13_relat_1]) ).
cnf(c_33,plain,
( in(sK0(A,B,C,D),B)
| ~ in(D,C)
| relation_image(A,B) != C
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d13_relat_1]) ).
cnf(c_34,plain,
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A)
| in(D,C)
| relation_image(A,B) != C
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d13_relat_1]) ).
cnf(c_39,plain,
( ~ in(ordered_pair(C,D),A)
| in(C,B)
| relation_dom(A) != B
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_relat_1]) ).
fof(nnf_30,plain,
? [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(D,A),C)
| ~ in(D,relation_dom(C)) )
| ~ in(A,relation_image(C,B)) )
& ( ? [X3] :
( in(X3,B)
& in(ordered_pair(X3,A),C)
& in(X3,relation_dom(C)) )
| in(A,relation_image(C,B)) )
& relation(C) ),
inference(fof_nnf,[status(thm)],[t143_relat_1_neg]) ).
fof(sk_t143_relat_1_neg_sk,plain,
( ( ! [D] :
( ~ in(D,sK3)
| ~ in(ordered_pair(D,sK2),sK1)
| ~ in(D,relation_dom(sK1)) )
| ~ in(sK2,relation_image(sK1,sK3)) )
& ( ( in(sK4,sK3)
& in(ordered_pair(sK4,sK2),sK1)
& in(sK4,relation_dom(sK1)) )
| in(sK2,relation_image(sK1,sK3)) )
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK1),skolemize(X3,sK4)],[nnf_30]) ).
fof(sk_t143_relat_1_neg,plain,
( ! [VAR_0] :
( ~ in(VAR_0,sK3)
| ~ in(ordered_pair(VAR_0,sK2),sK1)
| ~ in(VAR_0,relation_dom(sK1))
| ~ in(sK2,relation_image(sK1,sK3)) )
& ( in(sK4,sK3)
| in(sK2,relation_image(sK1,sK3)) )
& ( in(ordered_pair(sK4,sK2),sK1)
| in(sK2,relation_image(sK1,sK3)) )
& ( in(sK4,relation_dom(sK1))
| in(sK2,relation_image(sK1,sK3)) )
& relation(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_t143_relat_1_neg_sk]) ).
cnf(c_47,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t143_relat_1_neg]) ).
cnf(c_53,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_54,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_69,negated_conjecture,
( in(ordered_pair(sK4,sK2),sK1)
| in(sK2,relation_image(sK1,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t143_relat_1_neg]) ).
cnf(c_3158,negated_conjecture,
( in(unordered_pair(unordered_pair(sK4,sK2),singleton(sK4)),sK1)
| in(sK2,relation_image(sK1,sK3)) ),
inference(paramod,[status(thm)],[c_54,c_69]) ).
cnf(c_70,negated_conjecture,
( in(unordered_pair(unordered_pair(sK2,sK4),singleton(sK4)),sK1)
| in(sK2,relation_image(sK1,sK3)) ),
inference(paramod,[status(thm)],[c_53,c_3158]) ).
cnf(c_71,negated_conjecture,
( in(sK4,sK3)
| in(sK2,relation_image(sK1,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t143_relat_1_neg]) ).
cnf(c_72,negated_conjecture,
( ~ in(A,sK3)
| ~ in(ordered_pair(A,sK2),sK1)
| ~ in(A,relation_dom(sK1))
| ~ in(sK2,relation_image(sK1,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t143_relat_1_neg]) ).
cnf(c_73,negated_conjecture,
( ~ in(A,sK3)
| ~ in(unordered_pair(unordered_pair(A,sK2),singleton(A)),sK1)
| ~ in(A,relation_dom(sK1))
| ~ in(sK2,relation_image(sK1,sK3)) ),
inference(paramod,[status(thm)],[c_54,c_72]) ).
cnf(c_163,negated_conjecture,
( ~ in(ordered_pair(B,C),sK1)
| in(B,A)
| relation_dom(sK1) != A ),
inference(resolve,[status(thm)],[c_47,c_39]) ).
cnf(c_164,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(B,C),singleton(B)),sK1)
| in(B,A)
| relation_dom(sK1) != A ),
inference(paramod,[status(thm)],[c_54,c_163]) ).
cnf(c_172,negated_conjecture,
( ~ in(D,A)
| ~ in(ordered_pair(D,C),sK1)
| in(C,B)
| relation_image(sK1,A) != B ),
inference(resolve,[status(thm)],[c_47,c_34]) ).
cnf(c_173,negated_conjecture,
( ~ in(D,A)
| ~ in(unordered_pair(unordered_pair(D,C),singleton(D)),sK1)
| in(C,B)
| relation_image(sK1,A) != B ),
inference(paramod,[status(thm)],[c_54,c_172]) ).
cnf(c_174,negated_conjecture,
( in(sK0(sK1,A,B,C),A)
| ~ in(C,B)
| relation_image(sK1,A) != B ),
inference(resolve,[status(thm)],[c_47,c_33]) ).
cnf(c_175,negated_conjecture,
( in(ordered_pair(sK0(sK1,A,B,C),C),sK1)
| ~ in(C,B)
| relation_image(sK1,A) != B ),
inference(resolve,[status(thm)],[c_47,c_31]) ).
cnf(c_3159,negated_conjecture,
( in(unordered_pair(unordered_pair(sK0(sK1,A,B,C),C),singleton(sK0(sK1,A,B,C))),sK1)
| ~ in(C,B)
| relation_image(sK1,A) != B ),
inference(paramod,[status(thm)],[c_54,c_175]) ).
cnf(c_176,negated_conjecture,
( in(unordered_pair(unordered_pair(C,sK0(sK1,A,B,C)),singleton(sK0(sK1,A,B,C))),sK1)
| ~ in(C,B)
| relation_image(sK1,A) != B ),
inference(paramod,[status(thm)],[c_53,c_3159]) ).
cnf(c_202,plain,
( ~ in(A,sK3)
| ~ in(unordered_pair(unordered_pair(sK2,A),singleton(A)),sK1)
| ~ in(A,relation_dom(sK1))
| ~ in(sK2,relation_image(sK1,sK3)) ),
inference(paramod,[status(thm)],[c_53,c_73]) ).
cnf(c_339,plain,
( ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),sK1)
| in(A,relation_dom(sK1)) ),
inference(xxres,[status(thm)],[c_164]) ).
cnf(c_388,plain,
( in(sK2,relation_image(sK1,sK3))
| ~ in(unordered_pair(unordered_pair(sK4,B),singleton(sK4)),sK1)
| in(B,A)
| relation_image(sK1,sK3) != A ),
inference(resolve,[status(thm)],[c_173,c_71]) ).
cnf(c_3160,plain,
( ~ in(unordered_pair(unordered_pair(sK4,sK2),singleton(sK4)),sK1)
| in(sK2,relation_image(sK1,sK3))
| relation_image(sK1,sK3) != relation_image(sK1,sK3) ),
inference(factor,[status(thm)],[c_388]) ).
cnf(c_3161,plain,
( ~ in(unordered_pair(unordered_pair(sK2,sK4),singleton(sK4)),sK1)
| in(sK2,relation_image(sK1,sK3))
| relation_image(sK1,sK3) != relation_image(sK1,sK3) ),
inference(paramod,[status(thm)],[c_53,c_3160]) ).
cnf(c_397,plain,
( ~ in(unordered_pair(unordered_pair(sK2,sK4),singleton(sK4)),sK1)
| in(sK2,relation_image(sK1,sK3)) ),
inference(copy,[status(thm)],[c_3161]) ).
cnf(c_399,plain,
( in(sK0(sK1,B,relation_image(sK1,B),A),B)
| ~ in(A,relation_image(sK1,B)) ),
inference(xxres,[status(thm)],[c_174]) ).
cnf(c_410,plain,
( in(unordered_pair(unordered_pair(A,sK0(sK1,B,relation_image(sK1,B),A)),singleton(sK0(sK1,B,relation_image(sK1,B),A))),sK1)
| ~ in(A,relation_image(sK1,B)) ),
inference(xxres,[status(thm)],[c_176]) ).
cnf(c_829,plain,
( ~ in(unordered_pair(unordered_pair(B,A),singleton(A)),sK1)
| in(A,relation_dom(sK1)) ),
inference(paramod,[status(thm)],[c_53,c_339]) ).
cnf(c_3162,negated_conjecture,
( in(sK2,relation_image(sK1,sK3))
| in(sK2,relation_image(sK1,sK3)) ),
inference(resolve,[status(thm)],[c_397,c_70]) ).
cnf(c_927,negated_conjecture,
in(sK2,relation_image(sK1,sK3)),
inference(copy,[status(thm)],[c_3162]) ).
cnf(c_944,plain,
( ~ in(A,sK3)
| ~ in(unordered_pair(unordered_pair(sK2,A),singleton(A)),sK1)
| ~ in(A,relation_dom(sK1)) ),
inference(resolve,[status(thm)],[c_927,c_202]) ).
cnf(c_949,plain,
in(sK0(sK1,sK3,relation_image(sK1,sK3),sK2),sK3),
inference(resolve,[status(thm)],[c_927,c_399]) ).
cnf(c_1346,plain,
( ~ in(unordered_pair(unordered_pair(sK2,sK0(sK1,sK3,relation_image(sK1,sK3),sK2)),singleton(sK0(sK1,sK3,relation_image(sK1,sK3),sK2))),sK1)
| ~ in(sK0(sK1,sK3,relation_image(sK1,sK3),sK2),relation_dom(sK1)) ),
inference(resolve,[status(thm)],[c_944,c_949]) ).
cnf(c_3143,plain,
in(unordered_pair(unordered_pair(sK2,sK0(sK1,sK3,relation_image(sK1,sK3),sK2)),singleton(sK0(sK1,sK3,relation_image(sK1,sK3),sK2))),sK1),
inference(resolve,[status(thm)],[c_410,c_927]) ).
cnf(c_3153,plain,
~ in(sK0(sK1,sK3,relation_image(sK1,sK3),sK2),relation_dom(sK1)),
inference(resolve,[status(thm)],[c_3143,c_1346]) ).
cnf(c_3156,plain,
~ in(unordered_pair(unordered_pair(A,sK0(sK1,sK3,relation_image(sK1,sK3),sK2)),singleton(sK0(sK1,sK3,relation_image(sK1,sK3),sK2))),sK1),
inference(resolve,[status(thm)],[c_829,c_3153]) ).
cnf(c_3157,plain,
$false,
inference(resolve,[status(thm)],[c_3156,c_3143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU203+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.42 % Computer : n001.cluster.edu
% 0.08/0.42 % Model : x86_64 x86_64
% 0.08/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.42 % Memory : 8046.5625MB
% 0.08/0.42 % OS : Linux 6.8.0-71-generic
% 0.08/0.42 % CPULimit : 300
% 0.08/0.42 % WCLimit : 300
% 0.08/0.42 % DateTime : Sat Sep 26 08:54:42 UTC 2026
% 0.08/0.42 % CPUTime :
% 0.08/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.43 % Process 1417720 was started by sandbox on n001,
% 0.08/0.43 % Sat Sep 26 08:54:42 2026
% 0.08/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.43
% 0.08/0.43 % From the command line: assign(max_seconds, 300).
% 8.28/2.79
% 8.28/2.79 % given #500 (F,wt=36): 2191 -in(relation_dom(c7),f1(c7,relation_dom(c7),relation_image(c7,relation_dom(c7)),f2(c7,relation_dom(c7),empty_set))). [ur(2142,a,1208,a)].
% 8.28/2.79
% 8.28/2.79 % SZS status Theorem for theBenchmark
% 8.28/2.79
% 8.28/2.79 % Proof 1 at 0.95 (+ 0.11) seconds.
% 8.28/2.79 % Length of proof is 39.
% 8.28/2.79 % Level of proof is 11.
% 8.28/2.79 % Maximum clause weight is 60.000.
% 8.28/2.79 % Given clauses 640.
% 8.28/2.79
% 8.28/2.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------