%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU027+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 08:44:55 AM UTC 2026
% Result : Theorem 6.84s 1.37s
% Output : CNFRefutation 6.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 83 ( 20 unt; 0 def)
% Number of atoms : 380 ( 168 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 508 ( 211 ~; 216 |; 57 &)
% ( 5 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d5_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(t9_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( ! [C] :
( in(C,relation_dom(A))
=> apply(A,C) = apply(B,C) )
& relation_dom(A) = relation_dom(B) )
=> A = B ) ) ),
file('theBenchmark.p',t9_funct_1) ).
fof(t60_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( ! [C,D] :
( ( in(D,relation_dom(B))
& in(C,relation_dom(A)) )
=> ( apply(A,C) = D
<=> apply(B,D) = C ) )
& relation_rng(A) = relation_dom(B)
& relation_dom(A) = relation_rng(B)
& one_to_one(A) )
=> B = function_inverse(A) ) ) ),
file('theBenchmark.p',t60_funct_1) ).
fof(t60_funct_1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( ! [C,D] :
( ( in(D,relation_dom(B))
& in(C,relation_dom(A)) )
=> ( apply(A,C) = D
<=> apply(B,D) = C ) )
& relation_rng(A) = relation_dom(B)
& relation_dom(A) = relation_rng(B)
& one_to_one(A) )
=> B = function_inverse(A) ) ) ),
inference(assume_negation,[status(cth)],[t60_funct_1]) ).
cnf(c_37,plain,
( relation_dom(B) = relation_rng(A)
| 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_43,plain,
( apply(B,D) = C
| apply(A,C) != D
| ~ in(C,relation_dom(A))
| function_inverse(A) != B
| ~ function(B)
| ~ relation(B)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t54_funct_1]) ).
fof(nnf_36,plain,
? [A] :
( ? [B] :
( function_inverse(A) != B
& ! [C,D] :
( ( ( apply(B,D) != C
| apply(A,C) = D )
& ( apply(B,D) = C
| apply(A,C) != D ) )
| ~ in(D,relation_dom(B))
| ~ in(C,relation_dom(A)) )
& relation_dom(B) = relation_rng(A)
& relation_dom(A) = relation_rng(B)
& one_to_one(A)
& function(B)
& relation(B) )
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t60_funct_1_neg]) ).
fof(sk_t60_funct_1_neg_sk,plain,
( function_inverse(sK0) != sK1
& ! [C,D] :
( ( ( apply(sK1,D) != C
| apply(sK0,C) = D )
& ( apply(sK1,D) = C
| apply(sK0,C) != D ) )
| ~ in(D,relation_dom(sK1))
| ~ in(C,relation_dom(sK0)) )
& relation_dom(sK1) = relation_rng(sK0)
& relation_dom(sK0) = relation_rng(sK1)
& one_to_one(sK0)
& function(sK1)
& relation(sK1)
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_36]) ).
fof(sk_t60_funct_1_neg,plain,
( function_inverse(sK0) != sK1
& ! [VAR_0,VAR_1] :
( apply(sK1,VAR_1) != VAR_0
| apply(sK0,VAR_0) = VAR_1
| ~ in(VAR_1,relation_dom(sK1))
| ~ in(VAR_0,relation_dom(sK0)) )
& ! [VAR_0,VAR_1] :
( apply(sK1,VAR_1) = VAR_0
| apply(sK0,VAR_0) != VAR_1
| ~ in(VAR_1,relation_dom(sK1))
| ~ in(VAR_0,relation_dom(sK0)) )
& relation_dom(sK1) = relation_rng(sK0)
& relation_dom(sK0) = relation_rng(sK1)
& one_to_one(sK0)
& function(sK1)
& relation(sK1)
& function(sK0)
& relation(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_t60_funct_1_neg_sk]) ).
cnf(c_49,negated_conjecture,
one_to_one(sK0),
inference(split_conjunct,[status(thm)],[sk_t60_funct_1_neg]) ).
cnf(c_54,negated_conjecture,
( relation_dom(A) = relation_rng(sK0)
| function_inverse(sK0) != A
| ~ function(A)
| ~ relation(A)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_49,c_37]) ).
cnf(c_58,negated_conjecture,
( apply(A,C) = B
| apply(sK0,B) != C
| ~ in(B,relation_dom(sK0))
| function_inverse(sK0) != A
| ~ function(A)
| ~ relation(A)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_49,c_43]) ).
cnf(c_94,negated_conjecture,
function_inverse(sK0) != sK1,
inference(split_conjunct,[status(thm)],[sk_t60_funct_1_neg]) ).
cnf(c_95,negated_conjecture,
( apply(sK1,B) != A
| apply(sK0,A) = B
| ~ in(B,relation_dom(sK1))
| ~ in(A,relation_dom(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_t60_funct_1_neg]) ).
cnf(c_97,negated_conjecture,
relation_dom(sK1) = relation_rng(sK0),
inference(split_conjunct,[status(thm)],[sk_t60_funct_1_neg]) ).
cnf(c_98,negated_conjecture,
relation_rng(sK0) = relation_dom(sK1),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_99,negated_conjecture,
relation_dom(sK0) = relation_rng(sK1),
inference(split_conjunct,[status(thm)],[sk_t60_funct_1_neg]) ).
cnf(c_100,negated_conjecture,
relation_rng(sK1) = relation_dom(sK0),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_101,negated_conjecture,
function(sK1),
inference(split_conjunct,[status(thm)],[sk_t60_funct_1_neg]) ).
cnf(c_102,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t60_funct_1_neg]) ).
cnf(c_103,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t60_funct_1_neg]) ).
cnf(c_104,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t60_funct_1_neg]) ).
fof(nnf_35,plain,
! [A] :
( ! [B] :
( B = A
| ? [C] :
( apply(B,C) != apply(A,C)
& in(C,relation_dom(A)) )
| relation_dom(B) != relation_dom(A)
| ~ function(B)
| ~ relation(B) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t9_funct_1]) ).
fof(sk_t9_funct_1_sk,plain,
! [A] :
( ! [B] :
( B = A
| ( apply(B,sK2(A,B)) != apply(A,sK2(A,B))
& in(sK2(A,B),relation_dom(A)) )
| relation_dom(B) != relation_dom(A)
| ~ function(B)
| ~ relation(B) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(C,sK2(A,B))],[nnf_35]) ).
fof(sk_t9_funct_1,plain,
( ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| apply(VAR_1,sK2(VAR_0,VAR_1)) != apply(VAR_0,sK2(VAR_0,VAR_1))
| relation_dom(VAR_1) != relation_dom(VAR_0)
| ~ function(VAR_1)
| ~ relation(VAR_1)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| in(sK2(VAR_0,VAR_1),relation_dom(VAR_0))
| relation_dom(VAR_1) != relation_dom(VAR_0)
| ~ function(VAR_1)
| ~ relation(VAR_1)
| ~ function(VAR_0)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_t9_funct_1_sk]) ).
cnf(c_105,plain,
( B = A
| apply(B,sK2(A,B)) != apply(A,sK2(A,B))
| relation_dom(B) != relation_dom(A)
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_t9_funct_1]) ).
cnf(c_106,plain,
( B = A
| in(sK2(A,B),relation_dom(A))
| relation_dom(B) != relation_dom(A)
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_t9_funct_1]) ).
cnf(c_142,plain,
( function(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_143,plain,
( relation(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_148,plain,
( apply(A,D) != C
| ~ in(D,relation_dom(A))
| in(C,B)
| relation_rng(A) != B
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_funct_1]) ).
cnf(c_3084,negated_conjecture,
( relation_dom(A) = relation_dom(sK1)
| function_inverse(sK0) != A
| ~ function(A)
| ~ relation(A)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(paramod,[status(thm)],[c_98,c_54]) ).
cnf(c_3085,negated_conjecture,
( relation_dom(sK1) = relation_dom(A)
| function_inverse(sK0) != A
| ~ function(A)
| ~ relation(A)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(copy,[status(thm)],[c_3084]) ).
cnf(c_3086,negated_conjecture,
( relation_dom(sK1) = relation_dom(A)
| function_inverse(sK0) != A
| ~ function(A)
| ~ relation(A)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_104,c_3085]) ).
cnf(c_192,negated_conjecture,
( relation_dom(sK1) = relation_dom(A)
| function_inverse(sK0) != A
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_103,c_3086]) ).
cnf(c_3087,negated_conjecture,
( apply(A,C) = B
| apply(sK0,B) != C
| ~ in(B,relation_dom(sK0))
| function_inverse(sK0) != A
| ~ function(A)
| ~ relation(A)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_104,c_58]) ).
cnf(c_193,negated_conjecture,
( apply(A,C) = B
| apply(sK0,B) != C
| ~ in(B,relation_dom(sK0))
| function_inverse(sK0) != A
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_103,c_3087]) ).
cnf(c_3088,negated_conjecture,
( A = sK1
| apply(A,sK2(sK1,A)) != apply(sK1,sK2(sK1,A))
| relation_dom(A) != relation_dom(sK1)
| ~ function(A)
| ~ relation(A)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_105,c_101]) ).
cnf(c_3089,negated_conjecture,
( A = sK1
| apply(A,sK2(sK1,A)) != apply(sK1,sK2(sK1,A))
| relation_dom(sK1) != relation_dom(A)
| ~ function(A)
| ~ relation(A)
| ~ relation(sK1) ),
inference(copy,[status(thm)],[c_3088]) ).
cnf(c_3090,negated_conjecture,
( A = sK1
| apply(sK1,sK2(sK1,A)) != apply(A,sK2(sK1,A))
| relation_dom(sK1) != relation_dom(A)
| ~ function(A)
| ~ relation(A)
| ~ relation(sK1) ),
inference(copy,[status(thm)],[c_3089]) ).
cnf(c_3091,negated_conjecture,
( sK1 = A
| apply(sK1,sK2(sK1,A)) != apply(A,sK2(sK1,A))
| relation_dom(sK1) != relation_dom(A)
| ~ function(A)
| ~ relation(A)
| ~ relation(sK1) ),
inference(copy,[status(thm)],[c_3090]) ).
cnf(c_209,negated_conjecture,
( sK1 = A
| apply(sK1,sK2(sK1,A)) != apply(A,sK2(sK1,A))
| relation_dom(sK1) != relation_dom(A)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_102,c_3091]) ).
cnf(c_3092,negated_conjecture,
( A = sK1
| in(sK2(sK1,A),relation_dom(sK1))
| relation_dom(A) != relation_dom(sK1)
| ~ function(A)
| ~ relation(A)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_106,c_101]) ).
cnf(c_3093,negated_conjecture,
( A = sK1
| in(sK2(sK1,A),relation_dom(sK1))
| relation_dom(sK1) != relation_dom(A)
| ~ function(A)
| ~ relation(A)
| ~ relation(sK1) ),
inference(copy,[status(thm)],[c_3092]) ).
cnf(c_3094,negated_conjecture,
( sK1 = A
| in(sK2(sK1,A),relation_dom(sK1))
| relation_dom(sK1) != relation_dom(A)
| ~ function(A)
| ~ relation(A)
| ~ relation(sK1) ),
inference(copy,[status(thm)],[c_3093]) ).
cnf(c_213,negated_conjecture,
( sK1 = A
| in(sK2(sK1,A),relation_dom(sK1))
| relation_dom(sK1) != relation_dom(A)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_102,c_3094]) ).
cnf(c_3095,negated_conjecture,
( function(function_inverse(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_142,c_103]) ).
cnf(c_279,negated_conjecture,
function(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_104,c_3095]) ).
cnf(c_3096,negated_conjecture,
( relation(function_inverse(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_143,c_103]) ).
cnf(c_283,negated_conjecture,
relation(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_104,c_3096]) ).
cnf(c_3097,negated_conjecture,
( relation_dom(sK1) = relation_dom(function_inverse(sK0))
| function_inverse(sK0) != function_inverse(sK0)
| ~ relation(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_279,c_192]) ).
cnf(c_3098,negated_conjecture,
( relation_dom(function_inverse(sK0)) = relation_dom(sK1)
| function_inverse(sK0) != function_inverse(sK0)
| ~ relation(function_inverse(sK0)) ),
inference(copy,[status(thm)],[c_3097]) ).
cnf(c_3099,negated_conjecture,
( relation_dom(function_inverse(sK0)) = relation_dom(sK1)
| ~ relation(function_inverse(sK0)) ),
inference(copy,[status(thm)],[c_3098]) ).
cnf(c_441,negated_conjecture,
relation_dom(function_inverse(sK0)) = relation_dom(sK1),
inference(resolve,[status(thm)],[c_283,c_3099]) ).
cnf(c_3100,plain,
( sK1 = function_inverse(sK0)
| apply(sK1,sK2(sK1,function_inverse(sK0))) != apply(function_inverse(sK0),sK2(sK1,function_inverse(sK0)))
| relation_dom(sK1) != relation_dom(function_inverse(sK0))
| ~ relation(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_209,c_279]) ).
cnf(c_3101,plain,
( sK1 = function_inverse(sK0)
| apply(sK1,sK2(sK1,function_inverse(sK0))) != apply(function_inverse(sK0),sK2(sK1,function_inverse(sK0)))
| relation_dom(sK1) != relation_dom(sK1)
| ~ relation(function_inverse(sK0)) ),
inference(paramod,[status(thm)],[c_441,c_3100]) ).
cnf(c_3102,plain,
( sK1 = function_inverse(sK0)
| apply(function_inverse(sK0),sK2(sK1,function_inverse(sK0))) != apply(sK1,sK2(sK1,function_inverse(sK0)))
| relation_dom(sK1) != relation_dom(sK1)
| ~ relation(function_inverse(sK0)) ),
inference(copy,[status(thm)],[c_3101]) ).
cnf(c_3103,plain,
( function_inverse(sK0) = sK1
| apply(function_inverse(sK0),sK2(sK1,function_inverse(sK0))) != apply(sK1,sK2(sK1,function_inverse(sK0)))
| relation_dom(sK1) != relation_dom(sK1)
| ~ relation(function_inverse(sK0)) ),
inference(copy,[status(thm)],[c_3102]) ).
cnf(c_3104,plain,
( function_inverse(sK0) = sK1
| apply(function_inverse(sK0),sK2(sK1,function_inverse(sK0))) != apply(sK1,sK2(sK1,function_inverse(sK0)))
| ~ relation(function_inverse(sK0)) ),
inference(copy,[status(thm)],[c_3103]) ).
cnf(c_3105,plain,
( function_inverse(sK0) = sK1
| apply(function_inverse(sK0),sK2(sK1,function_inverse(sK0))) != apply(sK1,sK2(sK1,function_inverse(sK0))) ),
inference(resolve,[status(thm)],[c_283,c_3104]) ).
cnf(c_491,negated_conjecture,
apply(function_inverse(sK0),sK2(sK1,function_inverse(sK0))) != apply(sK1,sK2(sK1,function_inverse(sK0))),
inference(resolve,[status(thm)],[c_94,c_3105]) ).
cnf(c_3106,plain,
( sK1 = function_inverse(sK0)
| in(sK2(sK1,function_inverse(sK0)),relation_dom(sK1))
| relation_dom(sK1) != relation_dom(function_inverse(sK0))
| ~ relation(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_213,c_279]) ).
cnf(c_3107,plain,
( sK1 = function_inverse(sK0)
| in(sK2(sK1,function_inverse(sK0)),relation_dom(sK1))
| relation_dom(sK1) != relation_dom(sK1)
| ~ relation(function_inverse(sK0)) ),
inference(paramod,[status(thm)],[c_441,c_3106]) ).
cnf(c_3108,plain,
( function_inverse(sK0) = sK1
| in(sK2(sK1,function_inverse(sK0)),relation_dom(sK1))
| relation_dom(sK1) != relation_dom(sK1)
| ~ relation(function_inverse(sK0)) ),
inference(copy,[status(thm)],[c_3107]) ).
cnf(c_3109,plain,
( function_inverse(sK0) = sK1
| in(sK2(sK1,function_inverse(sK0)),relation_dom(sK1))
| ~ relation(function_inverse(sK0)) ),
inference(copy,[status(thm)],[c_3108]) ).
cnf(c_3110,plain,
( function_inverse(sK0) = sK1
| in(sK2(sK1,function_inverse(sK0)),relation_dom(sK1)) ),
inference(resolve,[status(thm)],[c_283,c_3109]) ).
cnf(c_717,negated_conjecture,
in(sK2(sK1,function_inverse(sK0)),relation_dom(sK1)),
inference(resolve,[status(thm)],[c_94,c_3110]) ).
cnf(c_3111,negated_conjecture,
( apply(sK1,C) != B
| ~ in(C,relation_dom(sK1))
| in(B,A)
| relation_rng(sK1) != A
| ~ function(sK1) ),
inference(resolve,[status(thm)],[c_148,c_102]) ).
cnf(c_3112,negated_conjecture,
( apply(sK1,C) != B
| ~ in(C,relation_dom(sK1))
| in(B,A)
| relation_rng(sK1) != A ),
inference(resolve,[status(thm)],[c_3111,c_101]) ).
cnf(c_3113,negated_conjecture,
( apply(sK1,B) != A
| ~ in(B,relation_dom(sK1))
| in(A,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_3112,c_100]) ).
cnf(c_3114,negated_conjecture,
( apply(sK1,sK2(sK1,function_inverse(sK0))) != A
| in(A,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_3113,c_717]) ).
cnf(c_865,plain,
in(apply(sK1,sK2(sK1,function_inverse(sK0))),relation_dom(sK0)),
inference(xxres,[status(thm)],[c_3114]) ).
cnf(c_3115,negated_conjecture,
( apply(function_inverse(sK0),B) = A
| apply(sK0,A) != B
| ~ in(A,relation_dom(sK0))
| function_inverse(sK0) != function_inverse(sK0)
| ~ function(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_193,c_283]) ).
cnf(c_3116,negated_conjecture,
( apply(function_inverse(sK0),B) = A
| apply(sK0,A) != B
| ~ in(A,relation_dom(sK0))
| function_inverse(sK0) != function_inverse(sK0) ),
inference(resolve,[status(thm)],[c_3115,c_279]) ).
cnf(c_3117,plain,
( apply(function_inverse(sK0),B) = A
| apply(sK0,A) != B
| ~ in(A,relation_dom(sK0)) ),
inference(xxres,[status(thm)],[c_3116]) ).
cnf(c_3118,plain,
( apply(function_inverse(sK0),A) = apply(sK1,sK2(sK1,function_inverse(sK0)))
| apply(sK0,apply(sK1,sK2(sK1,function_inverse(sK0)))) != A ),
inference(resolve,[status(thm)],[c_3117,c_865]) ).
cnf(c_3076,plain,
apply(function_inverse(sK0),apply(sK0,apply(sK1,sK2(sK1,function_inverse(sK0))))) = apply(sK1,sK2(sK1,function_inverse(sK0))),
inference(xxres,[status(thm)],[c_3118]) ).
cnf(c_3119,negated_conjecture,
( apply(sK1,A) != apply(sK1,sK2(sK1,function_inverse(sK0)))
| apply(sK0,apply(sK1,sK2(sK1,function_inverse(sK0)))) = A
| ~ in(A,relation_dom(sK1)) ),
inference(resolve,[status(thm)],[c_95,c_865]) ).
cnf(c_3120,negated_conjecture,
( apply(sK1,sK2(sK1,function_inverse(sK0))) != apply(sK1,sK2(sK1,function_inverse(sK0)))
| apply(sK0,apply(sK1,sK2(sK1,function_inverse(sK0)))) = sK2(sK1,function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_3119,c_717]) ).
cnf(c_3080,plain,
apply(sK0,apply(sK1,sK2(sK1,function_inverse(sK0)))) = sK2(sK1,function_inverse(sK0)),
inference(xxres,[status(thm)],[c_3120]) ).
cnf(c_3121,plain,
apply(function_inverse(sK0),sK2(sK1,function_inverse(sK0))) = apply(sK1,sK2(sK1,function_inverse(sK0))),
inference(paramod,[status(thm)],[c_3080,c_3076]) ).
cnf(c_3083,plain,
$false,
inference(resolve,[status(thm)],[c_491,c_3121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU027+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 08:29:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3301700 was started by sandbox2 on n007,
% 0.10/0.37 % Sat Sep 26 08:29:09 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 6.84/1.37
% 6.84/1.37 % given #500 (T,wt=25): 2480 empty(f5(A)) | empty(A) | -in(A,f4(f5(A))). [resolve(2211,c,153,b)].
% 6.84/1.37
% 6.84/1.37 % SZS status Theorem for theBenchmark
% 6.84/1.37
% 6.84/1.37 % Proof 1 at 0.87 (+ 0.07) seconds.
% 6.84/1.37 % Length of proof is 38.
% 6.84/1.37 % Level of proof is 8.
% 6.84/1.37 % Maximum clause weight is 58.000.
% 6.84/1.37 % Given clauses 675.
% 6.84/1.37
% 6.84/1.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------