%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU208+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 : n010.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 08:45:25 AM UTC 2026
% Result : Theorem 9.48s 12.40s
% Output : CNFRefutation 9.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 11 unt; 0 def)
% Number of atoms : 205 ( 36 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 : 127 ( 2 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(d14_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) ) ),
file('theBenchmark.p',d14_relat_1) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_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(t166_relat_1,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) ) ),
file('theBenchmark.p',t166_relat_1) ).
fof(t166_relat_1_neg,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) ) ),
inference(assume_negation,[status(cth)],[t166_relat_1]) ).
fof(nnf_4,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| ~ in(D,C) )
& ( ? [X3] :
( in(X3,B)
& in(ordered_pair(D,X3),A) )
| in(D,C) ) )
| relation_inverse_image(A,B) = C )
& ( ! [X0] :
( ( ! [X2] :
( ~ in(X2,B)
| ~ in(ordered_pair(X0,X2),A) )
| in(X0,C) )
& ( ? [X1] :
( in(X1,B)
& in(ordered_pair(X0,X1),A) )
| ~ in(X0,C) ) )
| relation_inverse_image(A,B) != C ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d14_relat_1]) ).
fof(sk_d14_relat_1_sk,plain,
! [A] :
( ! [B,C] :
( ( ( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(sK5(A,B,C),E),A) )
| ~ in(sK5(A,B,C),C) )
& ( ( in(sK6(A,B,C),B)
& in(ordered_pair(sK5(A,B,C),sK6(A,B,C)),A) )
| in(sK5(A,B,C),C) ) )
| relation_inverse_image(A,B) = C )
& ( ! [X0] :
( ( ! [X2] :
( ~ in(X2,B)
| ~ in(ordered_pair(X0,X2),A) )
| in(X0,C) )
& ( ( in(sK0(A,B,C,X0),B)
& in(ordered_pair(X0,sK0(A,B,C,X0)),A) )
| ~ in(X0,C) ) )
| relation_inverse_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_d14_relat_1,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(VAR_3,VAR_1)
| ~ in(ordered_pair(sK5(VAR_0,VAR_1,VAR_2),VAR_3),VAR_0)
| ~ in(sK5(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_inverse_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_inverse_image(VAR_0,VAR_1) = VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(ordered_pair(sK5(VAR_0,VAR_1,VAR_2),sK6(VAR_0,VAR_1,VAR_2)),VAR_0)
| in(sK5(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_inverse_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_3,VAR_4),VAR_0)
| in(VAR_3,VAR_2)
| relation_inverse_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_inverse_image(VAR_0,VAR_1) != VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(ordered_pair(VAR_3,sK0(VAR_0,VAR_1,VAR_2,VAR_3)),VAR_0)
| ~ in(VAR_3,VAR_2)
| relation_inverse_image(VAR_0,VAR_1) != VAR_2
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d14_relat_1_sk]) ).
cnf(c_31,plain,
( in(ordered_pair(D,sK0(A,B,C,D)),A)
| ~ in(D,C)
| relation_inverse_image(A,B) != C
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d14_relat_1]) ).
cnf(c_33,plain,
( in(sK0(A,B,C,D),B)
| ~ in(D,C)
| relation_inverse_image(A,B) != C
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d14_relat_1]) ).
cnf(c_34,plain,
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A)
| in(D,C)
| relation_inverse_image(A,B) != C
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d14_relat_1]) ).
cnf(c_39,plain,
( ~ in(ordered_pair(D,C),A)
| in(C,B)
| relation_rng(A) != B
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_relat_1]) ).
fof(nnf_30,plain,
? [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) )
& ( ? [X3] :
( in(X3,B)
& in(ordered_pair(A,X3),C)
& in(X3,relation_rng(C)) )
| in(A,relation_inverse_image(C,B)) )
& relation(C) ),
inference(fof_nnf,[status(thm)],[t166_relat_1_neg]) ).
fof(sk_t166_relat_1_neg_sk,plain,
( ( ! [D] :
( ~ in(D,sK3)
| ~ in(ordered_pair(sK2,D),sK1)
| ~ in(D,relation_rng(sK1)) )
| ~ in(sK2,relation_inverse_image(sK1,sK3)) )
& ( ( in(sK4,sK3)
& in(ordered_pair(sK2,sK4),sK1)
& in(sK4,relation_rng(sK1)) )
| in(sK2,relation_inverse_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_t166_relat_1_neg,plain,
( ! [VAR_0] :
( ~ in(VAR_0,sK3)
| ~ in(ordered_pair(sK2,VAR_0),sK1)
| ~ in(VAR_0,relation_rng(sK1))
| ~ in(sK2,relation_inverse_image(sK1,sK3)) )
& ( in(sK4,sK3)
| in(sK2,relation_inverse_image(sK1,sK3)) )
& ( in(ordered_pair(sK2,sK4),sK1)
| in(sK2,relation_inverse_image(sK1,sK3)) )
& ( in(sK4,relation_rng(sK1))
| in(sK2,relation_inverse_image(sK1,sK3)) )
& relation(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_t166_relat_1_neg_sk]) ).
cnf(c_47,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t166_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(sK2,sK4),sK1)
| in(sK2,relation_inverse_image(sK1,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t166_relat_1_neg]) ).
cnf(c_70,negated_conjecture,
( in(unordered_pair(unordered_pair(sK2,sK4),singleton(sK2)),sK1)
| in(sK2,relation_inverse_image(sK1,sK3)) ),
inference(paramod,[status(thm)],[c_54,c_69]) ).
cnf(c_71,negated_conjecture,
( in(sK4,sK3)
| in(sK2,relation_inverse_image(sK1,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t166_relat_1_neg]) ).
cnf(c_72,negated_conjecture,
( ~ in(A,sK3)
| ~ in(ordered_pair(sK2,A),sK1)
| ~ in(A,relation_rng(sK1))
| ~ in(sK2,relation_inverse_image(sK1,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t166_relat_1_neg]) ).
cnf(c_73,negated_conjecture,
( ~ in(A,sK3)
| ~ in(unordered_pair(unordered_pair(sK2,A),singleton(sK2)),sK1)
| ~ in(A,relation_rng(sK1))
| ~ in(sK2,relation_inverse_image(sK1,sK3)) ),
inference(paramod,[status(thm)],[c_54,c_72]) ).
cnf(c_163,negated_conjecture,
( ~ in(ordered_pair(C,B),sK1)
| in(B,A)
| relation_rng(sK1) != A ),
inference(resolve,[status(thm)],[c_47,c_39]) ).
cnf(c_164,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(C,B),singleton(C)),sK1)
| in(B,A)
| relation_rng(sK1) != A ),
inference(paramod,[status(thm)],[c_54,c_163]) ).
cnf(c_172,negated_conjecture,
( ~ in(D,A)
| ~ in(ordered_pair(C,D),sK1)
| in(C,B)
| relation_inverse_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(C,D),singleton(C)),sK1)
| in(C,B)
| relation_inverse_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_inverse_image(sK1,A) != B ),
inference(resolve,[status(thm)],[c_47,c_33]) ).
cnf(c_175,negated_conjecture,
( in(ordered_pair(C,sK0(sK1,A,B,C)),sK1)
| ~ in(C,B)
| relation_inverse_image(sK1,A) != B ),
inference(resolve,[status(thm)],[c_47,c_31]) ).
cnf(c_1431,negated_conjecture,
( in(unordered_pair(unordered_pair(C,sK0(sK1,A,B,C)),singleton(C)),sK1)
| ~ in(C,B)
| relation_inverse_image(sK1,A) != B ),
inference(paramod,[status(thm)],[c_54,c_175]) ).
cnf(c_176,negated_conjecture,
( in(unordered_pair(singleton(C),unordered_pair(C,sK0(sK1,A,B,C))),sK1)
| ~ in(C,B)
| relation_inverse_image(sK1,A) != B ),
inference(paramod,[status(thm)],[c_53,c_1431]) ).
cnf(c_201,plain,
( ~ in(A,sK3)
| ~ in(unordered_pair(singleton(sK2),unordered_pair(sK2,A)),sK1)
| ~ in(A,relation_rng(sK1))
| ~ in(sK2,relation_inverse_image(sK1,sK3)) ),
inference(paramod,[status(thm)],[c_53,c_73]) ).
cnf(c_332,plain,
( ~ in(unordered_pair(singleton(C),unordered_pair(C,B)),sK1)
| in(B,A)
| relation_rng(sK1) != A ),
inference(paramod,[status(thm)],[c_53,c_164]) ).
cnf(c_382,plain,
( in(sK2,relation_inverse_image(sK1,sK3))
| ~ in(unordered_pair(unordered_pair(B,sK4),singleton(B)),sK1)
| in(B,A)
| relation_inverse_image(sK1,sK3) != A ),
inference(resolve,[status(thm)],[c_173,c_71]) ).
cnf(c_1432,plain,
( ~ in(unordered_pair(unordered_pair(sK2,sK4),singleton(sK2)),sK1)
| in(sK2,relation_inverse_image(sK1,sK3))
| relation_inverse_image(sK1,sK3) != relation_inverse_image(sK1,sK3) ),
inference(factor,[status(thm)],[c_382]) ).
cnf(c_394,plain,
( ~ in(unordered_pair(unordered_pair(sK2,sK4),singleton(sK2)),sK1)
| in(sK2,relation_inverse_image(sK1,sK3)) ),
inference(copy,[status(thm)],[c_1432]) ).
cnf(c_1433,negated_conjecture,
( in(sK2,relation_inverse_image(sK1,sK3))
| in(sK2,relation_inverse_image(sK1,sK3)) ),
inference(resolve,[status(thm)],[c_394,c_70]) ).
cnf(c_601,negated_conjecture,
in(sK2,relation_inverse_image(sK1,sK3)),
inference(copy,[status(thm)],[c_1433]) ).
cnf(c_603,plain,
( ~ in(A,sK3)
| ~ in(unordered_pair(singleton(sK2),unordered_pair(sK2,A)),sK1)
| ~ in(A,relation_rng(sK1)) ),
inference(resolve,[status(thm)],[c_601,c_201]) ).
cnf(c_1434,negated_conjecture,
( in(unordered_pair(singleton(sK2),unordered_pair(sK2,sK0(sK1,A,relation_inverse_image(sK1,sK3),sK2))),sK1)
| relation_inverse_image(sK1,A) != relation_inverse_image(sK1,sK3) ),
inference(resolve,[status(thm)],[c_601,c_176]) ).
cnf(c_607,negated_conjecture,
( in(unordered_pair(singleton(sK2),unordered_pair(sK2,sK0(sK1,A,relation_inverse_image(sK1,sK3),sK2))),sK1)
| relation_inverse_image(sK1,sK3) != relation_inverse_image(sK1,A) ),
inference(copy,[status(thm)],[c_1434]) ).
cnf(c_1435,negated_conjecture,
( in(sK0(sK1,A,relation_inverse_image(sK1,sK3),sK2),A)
| relation_inverse_image(sK1,A) != relation_inverse_image(sK1,sK3) ),
inference(resolve,[status(thm)],[c_601,c_174]) ).
cnf(c_608,negated_conjecture,
( in(sK0(sK1,A,relation_inverse_image(sK1,sK3),sK2),A)
| relation_inverse_image(sK1,sK3) != relation_inverse_image(sK1,A) ),
inference(copy,[status(thm)],[c_1435]) ).
cnf(c_661,plain,
in(sK0(sK1,sK3,relation_inverse_image(sK1,sK3),sK2),sK3),
inference(xxres,[status(thm)],[c_608]) ).
cnf(c_1398,plain,
in(unordered_pair(singleton(sK2),unordered_pair(sK2,sK0(sK1,sK3,relation_inverse_image(sK1,sK3),sK2))),sK1),
inference(xxres,[status(thm)],[c_607]) ).
cnf(c_1436,plain,
( ~ in(sK0(sK1,sK3,relation_inverse_image(sK1,sK3),sK2),sK3)
| ~ in(sK0(sK1,sK3,relation_inverse_image(sK1,sK3),sK2),relation_rng(sK1)) ),
inference(resolve,[status(thm)],[c_1398,c_603]) ).
cnf(c_1401,plain,
~ in(sK0(sK1,sK3,relation_inverse_image(sK1,sK3),sK2),relation_rng(sK1)),
inference(resolve,[status(thm)],[c_661,c_1436]) ).
cnf(c_1405,plain,
( in(sK0(sK1,sK3,relation_inverse_image(sK1,sK3),sK2),A)
| relation_rng(sK1) != A ),
inference(resolve,[status(thm)],[c_1398,c_332]) ).
cnf(c_1437,plain,
in(sK0(sK1,sK3,relation_inverse_image(sK1,sK3),sK2),relation_rng(sK1)),
inference(xxres,[status(thm)],[c_1405]) ).
cnf(c_1430,plain,
$false,
inference(resolve,[status(thm)],[c_1401,c_1437]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU208+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/11.03 % Computer : n010.cluster.edu
% 0.13/11.03 % Model : x86_64 x86_64
% 0.13/11.03 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/11.03 % Memory : 8046.5625MB
% 0.13/11.03 % OS : Linux 6.8.0-71-generic
% 0.13/11.03 % CPULimit : 300
% 0.13/11.03 % WCLimit : 300
% 0.13/11.03 % DateTime : Sat Sep 26 08:50:25 UTC 2026
% 0.13/11.04 % CPUTime :
% 0.13/11.04 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/11.04 % Process 2947717 was started by sandbox2 on n010,
% 0.13/11.04 % Sat Sep 26 08:50:25 2026
% 0.13/11.04 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/11.05
% 0.18/11.05 % From the command line: assign(max_seconds, 300).
% 9.48/12.40
% 9.48/12.40 % SZS status Theorem for theBenchmark
% 9.48/12.40
% 9.48/12.40 % Proof 1 at 1.24 (+ 0.09) seconds.
% 9.48/12.40 % Length of proof is 37.
% 9.48/12.40 % Level of proof is 10.
% 9.48/12.40 % Maximum clause weight is 21.000.
% 9.48/12.40 % Given clauses 419.
% 9.48/12.40
% 9.48/12.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------