%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU023+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 : 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 08:44:54 AM UTC 2026
% Result : Theorem 0.81s 0.59s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 11 unt; 0 def)
% Number of atoms : 140 ( 52 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 171 ( 69 ~; 62 |; 26 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 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 : 45 ( 0 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(t23_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('theBenchmark.p',t23_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(t56_funct_1,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_dom(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(B,function_inverse(B)),A)
& A = apply(function_inverse(B),apply(B,A)) ) ) ),
file('theBenchmark.p',t56_funct_1) ).
fof(t56_funct_1_neg,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_dom(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(B,function_inverse(B)),A)
& A = apply(function_inverse(B),apply(B,A)) ) ) ),
inference(assume_negation,[status(cth)],[t56_funct_1]) ).
cnf(c_46,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_39,plain,
? [A,B] :
( ( apply(relation_composition(B,function_inverse(B)),A) != A
| apply(function_inverse(B),apply(B,A)) != A )
& in(A,relation_dom(B))
& one_to_one(B)
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t56_funct_1_neg]) ).
fof(sk_t56_funct_1_neg,plain,
( ( apply(relation_composition(sK0,function_inverse(sK0)),sK1) != sK1
| apply(function_inverse(sK0),apply(sK0,sK1)) != sK1 )
& in(sK1,relation_dom(sK0))
& one_to_one(sK0)
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_39]) ).
cnf(c_52,negated_conjecture,
one_to_one(sK0),
inference(split_conjunct,[status(thm)],[sk_t56_funct_1_neg]) ).
cnf(c_61,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_52,c_46]) ).
cnf(c_97,negated_conjecture,
( apply(relation_composition(sK0,function_inverse(sK0)),sK1) != sK1
| apply(function_inverse(sK0),apply(sK0,sK1)) != sK1 ),
inference(split_conjunct,[status(thm)],[sk_t56_funct_1_neg]) ).
cnf(c_98,negated_conjecture,
in(sK1,relation_dom(sK0)),
inference(split_conjunct,[status(thm)],[sk_t56_funct_1_neg]) ).
cnf(c_99,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t56_funct_1_neg]) ).
cnf(c_100,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t56_funct_1_neg]) ).
cnf(c_107,plain,
( apply(relation_composition(A,B),C) = apply(B,apply(A,C))
| ~ in(C,relation_dom(A))
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t23_funct_1]) ).
cnf(c_144,plain,
( function(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_145,plain,
( relation(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_615,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_100,c_61]) ).
cnf(c_184,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_99,c_615]) ).
cnf(c_616,negated_conjecture,
( function(function_inverse(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_144,c_99]) ).
cnf(c_334,negated_conjecture,
function(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_100,c_616]) ).
cnf(c_617,negated_conjecture,
( relation(function_inverse(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_145,c_99]) ).
cnf(c_337,negated_conjecture,
relation(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_100,c_617]) ).
cnf(c_618,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_184,c_337]) ).
cnf(c_619,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_618,c_334]) ).
cnf(c_620,plain,
( apply(function_inverse(sK0),B) = A
| apply(sK0,A) != B
| ~ in(A,relation_dom(sK0)) ),
inference(xxres,[status(thm)],[c_619]) ).
cnf(c_621,negated_conjecture,
( apply(function_inverse(sK0),A) = sK1
| apply(sK0,sK1) != A ),
inference(resolve,[status(thm)],[c_620,c_98]) ).
cnf(c_580,plain,
apply(function_inverse(sK0),apply(sK0,sK1)) = sK1,
inference(xxres,[status(thm)],[c_621]) ).
cnf(c_622,negated_conjecture,
( apply(relation_composition(sK0,A),B) = apply(A,apply(sK0,B))
| ~ in(B,relation_dom(sK0))
| ~ function(A)
| ~ relation(A)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_107,c_100]) ).
cnf(c_623,negated_conjecture,
( apply(relation_composition(sK0,A),B) = apply(A,apply(sK0,B))
| ~ in(B,relation_dom(sK0))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_622,c_99]) ).
cnf(c_624,negated_conjecture,
( apply(relation_composition(sK0,function_inverse(sK0)),A) = apply(function_inverse(sK0),apply(sK0,A))
| ~ in(A,relation_dom(sK0))
| ~ function(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_623,c_337]) ).
cnf(c_625,negated_conjecture,
( apply(relation_composition(sK0,function_inverse(sK0)),A) = apply(function_inverse(sK0),apply(sK0,A))
| ~ in(A,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_624,c_334]) ).
cnf(c_626,negated_conjecture,
apply(relation_composition(sK0,function_inverse(sK0)),sK1) = apply(function_inverse(sK0),apply(sK0,sK1)),
inference(resolve,[status(thm)],[c_625,c_98]) ).
cnf(c_611,negated_conjecture,
apply(relation_composition(sK0,function_inverse(sK0)),sK1) = sK1,
inference(paramod,[status(thm)],[c_580,c_626]) ).
cnf(c_627,negated_conjecture,
( apply(relation_composition(sK0,function_inverse(sK0)),sK1) != sK1
| sK1 != sK1 ),
inference(paramod,[status(thm)],[c_580,c_97]) ).
cnf(c_628,negated_conjecture,
( sK1 != sK1
| sK1 != sK1 ),
inference(paramod,[status(thm)],[c_611,c_627]) ).
cnf(c_629,negated_conjecture,
sK1 != sK1,
inference(copy,[status(thm)],[c_628]) ).
cnf(c_614,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_629]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU023+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 08:30:45 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 50202 was started by sandbox2 on n011,
% 0.10/0.36 % Sat Sep 26 08:30:45 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.81/0.59
% 0.81/0.59 % SZS status Theorem for theBenchmark
% 0.81/0.59
% 0.81/0.59 % Proof 1 at 0.18 (+ 0.03) seconds.
% 0.81/0.59 % Length of proof is 20.
% 0.81/0.59 % Level of proof is 6.
% 0.81/0.59 % Maximum clause weight is 43.000.
% 0.81/0.59 % Given clauses 143.
% 0.81/0.59
% 0.81/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------