%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU221+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 : n011.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 08:45:28 AM UTC 2026
% Result : Theorem 60.53s 8.19s
% Output : CNFRefutation 60.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 60 ( 16 unt; 0 def)
% Number of atoms : 225 ( 51 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 271 ( 106 ~; 113 |; 36 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 25 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d8_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('theBenchmark.p',d8_funct_1) ).
fof(dt_k2_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('theBenchmark.p',dt_k2_funct_1) ).
fof(t54_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('theBenchmark.p',t54_funct_1) ).
fof(t57_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_rng(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) ) ) ),
file('theBenchmark.p',t57_funct_1) ).
fof(t62_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('theBenchmark.p',t62_funct_1) ).
fof(t62_funct_1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
inference(assume_negation,[status(cth)],[t62_funct_1]) ).
fof(nnf_5,plain,
! [A] :
( ( ( ? [B,C] :
( C != B
& apply(A,C) = apply(A,B)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
| one_to_one(A) )
& ( ! [X0,X1] :
( X1 = X0
| apply(A,X1) != apply(A,X0)
| ~ in(X1,relation_dom(A))
| ~ in(X0,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_funct_1]) ).
fof(sk_d8_funct_1_sk,plain,
! [A] :
( ( ( ( sK1(A) != sK0(A)
& apply(A,sK1(A)) = apply(A,sK0(A))
& in(sK1(A),relation_dom(A))
& in(sK0(A),relation_dom(A)) )
| one_to_one(A) )
& ( ! [X0,X1] :
( X1 = X0
| apply(A,X1) != apply(A,X0)
| ~ in(X1,relation_dom(A))
| ~ in(X0,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0(A)),skolemize(C,sK1(A))],[nnf_5]) ).
fof(sk_d8_funct_1,plain,
( ! [VAR_0] :
( sK1(VAR_0) != sK0(VAR_0)
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( apply(VAR_0,sK1(VAR_0)) = apply(VAR_0,sK0(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( in(sK1(VAR_0),relation_dom(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( in(sK0(VAR_0),relation_dom(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| apply(VAR_0,VAR_2) != apply(VAR_0,VAR_1)
| ~ in(VAR_2,relation_dom(VAR_0))
| ~ in(VAR_1,relation_dom(VAR_0))
| ~ one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d8_funct_1_sk]) ).
cnf(c_47,plain,
( in(sK0(A),relation_dom(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_48,plain,
( in(sK1(A),relation_dom(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_49,plain,
( apply(A,sK1(A)) = apply(A,sK0(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_50,plain,
( sK1(A) != sK0(A)
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_51,plain,
( relation(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_52,plain,
( function(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_82,plain,
( relation_rng(A) = relation_dom(B)
| function_inverse(A) != B
| ~ function(B)
| ~ relation(B)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t54_funct_1]) ).
cnf(c_92,plain,
( apply(A,apply(function_inverse(A),B)) = B
| ~ in(B,relation_rng(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t57_funct_1]) ).
fof(nnf_38,plain,
? [A] :
( ~ one_to_one(function_inverse(A))
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t62_funct_1_neg]) ).
fof(sk_t62_funct_1_neg,plain,
( ~ one_to_one(function_inverse(sK2))
& one_to_one(sK2)
& function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(A,sK2)],[nnf_38]) ).
cnf(c_97,negated_conjecture,
relation(sK2),
inference(split_conjunct,[status(thm)],[sk_t62_funct_1_neg]) ).
cnf(c_98,negated_conjecture,
function(sK2),
inference(split_conjunct,[status(thm)],[sk_t62_funct_1_neg]) ).
cnf(c_99,negated_conjecture,
one_to_one(sK2),
inference(split_conjunct,[status(thm)],[sk_t62_funct_1_neg]) ).
cnf(c_100,negated_conjecture,
~ one_to_one(function_inverse(sK2)),
inference(split_conjunct,[status(thm)],[sk_t62_funct_1_neg]) ).
cnf(c_9315,plain,
( relation_rng(A) = relation_dom(function_inverse(A))
| ~ function(function_inverse(A))
| ~ relation(function_inverse(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(xxres,[status(thm)],[c_82]) ).
cnf(c_272,plain,
( relation_dom(function_inverse(A)) = relation_rng(A)
| ~ function(function_inverse(A))
| ~ relation(function_inverse(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(copy,[status(thm)],[c_9315]) ).
cnf(c_9316,negated_conjecture,
( function(function_inverse(sK2))
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_97,c_52]) ).
cnf(c_481,negated_conjecture,
function(function_inverse(sK2)),
inference(resolve,[status(thm)],[c_98,c_9316]) ).
cnf(c_9317,negated_conjecture,
( relation(function_inverse(sK2))
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_97,c_51]) ).
cnf(c_482,negated_conjecture,
relation(function_inverse(sK2)),
inference(resolve,[status(thm)],[c_98,c_9317]) ).
cnf(c_9318,plain,
( sK1(function_inverse(sK2)) != sK0(function_inverse(sK2))
| one_to_one(function_inverse(sK2))
| ~ relation(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_481,c_50]) ).
cnf(c_9319,plain,
( sK1(function_inverse(sK2)) != sK0(function_inverse(sK2))
| one_to_one(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_482,c_9318]) ).
cnf(c_758,negated_conjecture,
sK1(function_inverse(sK2)) != sK0(function_inverse(sK2)),
inference(resolve,[status(thm)],[c_100,c_9319]) ).
cnf(c_9320,plain,
( apply(function_inverse(sK2),sK1(function_inverse(sK2))) = apply(function_inverse(sK2),sK0(function_inverse(sK2)))
| one_to_one(function_inverse(sK2))
| ~ relation(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_481,c_49]) ).
cnf(c_9321,plain,
( apply(function_inverse(sK2),sK1(function_inverse(sK2))) = apply(function_inverse(sK2),sK0(function_inverse(sK2)))
| one_to_one(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_482,c_9320]) ).
cnf(c_759,negated_conjecture,
apply(function_inverse(sK2),sK1(function_inverse(sK2))) = apply(function_inverse(sK2),sK0(function_inverse(sK2))),
inference(resolve,[status(thm)],[c_100,c_9321]) ).
cnf(c_9322,plain,
( in(sK1(function_inverse(sK2)),relation_dom(function_inverse(sK2)))
| one_to_one(function_inverse(sK2))
| ~ relation(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_481,c_48]) ).
cnf(c_9323,plain,
( in(sK1(function_inverse(sK2)),relation_dom(function_inverse(sK2)))
| one_to_one(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_482,c_9322]) ).
cnf(c_760,negated_conjecture,
in(sK1(function_inverse(sK2)),relation_dom(function_inverse(sK2))),
inference(resolve,[status(thm)],[c_100,c_9323]) ).
cnf(c_9324,plain,
( in(sK0(function_inverse(sK2)),relation_dom(function_inverse(sK2)))
| one_to_one(function_inverse(sK2))
| ~ relation(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_481,c_47]) ).
cnf(c_9325,plain,
( in(sK0(function_inverse(sK2)),relation_dom(function_inverse(sK2)))
| one_to_one(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_482,c_9324]) ).
cnf(c_761,negated_conjecture,
in(sK0(function_inverse(sK2)),relation_dom(function_inverse(sK2))),
inference(resolve,[status(thm)],[c_100,c_9325]) ).
cnf(c_9326,negated_conjecture,
( relation_dom(function_inverse(sK2)) = relation_rng(sK2)
| ~ function(function_inverse(sK2))
| ~ relation(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_272,c_97]) ).
cnf(c_9327,negated_conjecture,
( relation_dom(function_inverse(sK2)) = relation_rng(sK2)
| ~ function(function_inverse(sK2))
| ~ relation(function_inverse(sK2))
| ~ one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_98,c_9326]) ).
cnf(c_9328,negated_conjecture,
( relation_dom(function_inverse(sK2)) = relation_rng(sK2)
| ~ function(function_inverse(sK2))
| ~ relation(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_99,c_9327]) ).
cnf(c_9329,negated_conjecture,
( relation_dom(function_inverse(sK2)) = relation_rng(sK2)
| ~ function(function_inverse(sK2)) ),
inference(resolve,[status(thm)],[c_482,c_9328]) ).
cnf(c_6739,negated_conjecture,
relation_dom(function_inverse(sK2)) = relation_rng(sK2),
inference(resolve,[status(thm)],[c_481,c_9329]) ).
cnf(c_6747,negated_conjecture,
in(sK0(function_inverse(sK2)),relation_rng(sK2)),
inference(paramod,[status(thm)],[c_6739,c_761]) ).
cnf(c_6748,negated_conjecture,
in(sK1(function_inverse(sK2)),relation_rng(sK2)),
inference(paramod,[status(thm)],[c_6739,c_760]) ).
cnf(c_9330,plain,
( apply(sK2,apply(function_inverse(sK2),sK0(function_inverse(sK2)))) = sK0(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_6747,c_92]) ).
cnf(c_9331,negated_conjecture,
( apply(sK2,apply(function_inverse(sK2),sK0(function_inverse(sK2)))) = sK0(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_97,c_9330]) ).
cnf(c_9332,negated_conjecture,
( apply(sK2,apply(function_inverse(sK2),sK0(function_inverse(sK2)))) = sK0(function_inverse(sK2))
| ~ one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_98,c_9331]) ).
cnf(c_9301,negated_conjecture,
apply(sK2,apply(function_inverse(sK2),sK0(function_inverse(sK2)))) = sK0(function_inverse(sK2)),
inference(resolve,[status(thm)],[c_99,c_9332]) ).
cnf(c_9333,plain,
( apply(sK2,apply(function_inverse(sK2),sK1(function_inverse(sK2)))) = sK1(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_6748,c_92]) ).
cnf(c_9334,plain,
( apply(sK2,apply(function_inverse(sK2),sK0(function_inverse(sK2)))) = sK1(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(paramod,[status(thm)],[c_759,c_9333]) ).
cnf(c_9335,plain,
( sK0(function_inverse(sK2)) = sK1(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(paramod,[status(thm)],[c_9301,c_9334]) ).
cnf(c_9336,plain,
( sK1(function_inverse(sK2)) = sK0(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(copy,[status(thm)],[c_9335]) ).
cnf(c_9337,negated_conjecture,
( sK1(function_inverse(sK2)) = sK0(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_97,c_9336]) ).
cnf(c_9338,negated_conjecture,
( sK1(function_inverse(sK2)) = sK0(function_inverse(sK2))
| ~ one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_98,c_9337]) ).
cnf(c_9339,negated_conjecture,
sK1(function_inverse(sK2)) = sK0(function_inverse(sK2)),
inference(resolve,[status(thm)],[c_99,c_9338]) ).
cnf(c_9314,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_758,c_9339]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU221+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n011.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 08:52:58 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 105950 was started by sandbox on n011,
% 0.18/0.45 % Sat Sep 26 08:52:58 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 60.53/8.19
% 60.53/8.19 % SZS status Theorem for theBenchmark
% 60.53/8.19
% 60.53/8.19 % Proof 1 at 7.14 (+ 0.51) seconds.
% 60.53/8.19 % Length of proof is 29.
% 60.53/8.19 % Level of proof is 6.
% 60.53/8.19 % Maximum clause weight is 40.000.
% 60.53/8.19 % Given clauses 445.
% 60.53/8.19
% 60.53/8.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------