%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU220+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 25.96s 3.83s
% Output : CNFRefutation 25.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 12 unt; 0 def)
% Number of atoms : 162 ( 58 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 198 ( 80 ~; 74 |; 28 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 2 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 : 49 ( 0 sgn 13 !; 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(t55_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('theBenchmark.p',t55_funct_1) ).
fof(t57_funct_1,conjecture,
! [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(t57_funct_1_neg,negated_conjecture,
~ ! [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)) ) ) ),
inference(assume_negation,[status(cth)],[t57_funct_1]) ).
cnf(c_45,plain,
( apply(A,D) = C
| apply(B,C) != D
| ~ in(C,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_53,plain,
( relation_rng(A) = relation_dom(function_inverse(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t55_funct_1]) ).
fof(nnf_40,plain,
? [A,B] :
( ( apply(relation_composition(function_inverse(B),B),A) != A
| apply(B,apply(function_inverse(B),A)) != A )
& in(A,relation_rng(B))
& one_to_one(B)
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t57_funct_1_neg]) ).
fof(sk_t57_funct_1_neg,plain,
( ( apply(relation_composition(function_inverse(sK0),sK0),sK1) != sK1
| apply(sK0,apply(function_inverse(sK0),sK1)) != sK1 )
& in(sK1,relation_rng(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_40]) ).
cnf(c_55,negated_conjecture,
one_to_one(sK0),
inference(split_conjunct,[status(thm)],[sk_t57_funct_1_neg]) ).
cnf(c_62,negated_conjecture,
( apply(sK0,C) = B
| apply(A,B) != C
| ~ in(B,relation_rng(sK0))
| function_inverse(sK0) != A
| ~ function(A)
| ~ relation(A)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_55,c_45]) ).
cnf(c_70,negated_conjecture,
( relation_rng(sK0) = relation_dom(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_55,c_53]) ).
cnf(c_71,negated_conjecture,
( relation_dom(function_inverse(sK0)) = relation_rng(sK0)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_110,negated_conjecture,
( apply(relation_composition(function_inverse(sK0),sK0),sK1) != sK1
| apply(sK0,apply(function_inverse(sK0),sK1)) != sK1 ),
inference(split_conjunct,[status(thm)],[sk_t57_funct_1_neg]) ).
cnf(c_111,negated_conjecture,
in(sK1,relation_rng(sK0)),
inference(split_conjunct,[status(thm)],[sk_t57_funct_1_neg]) ).
cnf(c_112,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t57_funct_1_neg]) ).
cnf(c_113,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t57_funct_1_neg]) ).
cnf(c_120,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_157,plain,
( function(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_158,plain,
( relation(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_7171,negated_conjecture,
( relation_dom(function_inverse(sK0)) = relation_rng(sK0)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_113,c_71]) ).
cnf(c_193,negated_conjecture,
relation_dom(function_inverse(sK0)) = relation_rng(sK0),
inference(resolve,[status(thm)],[c_112,c_7171]) ).
cnf(c_7172,negated_conjecture,
( apply(sK0,C) = B
| apply(A,B) != C
| ~ in(B,relation_rng(sK0))
| function_inverse(sK0) != A
| ~ function(A)
| ~ relation(A)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_113,c_62]) ).
cnf(c_201,negated_conjecture,
( apply(sK0,C) = B
| apply(A,B) != C
| ~ in(B,relation_rng(sK0))
| function_inverse(sK0) != A
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_112,c_7172]) ).
cnf(c_7173,negated_conjecture,
( function(function_inverse(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_157,c_112]) ).
cnf(c_351,negated_conjecture,
function(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_113,c_7173]) ).
cnf(c_7174,negated_conjecture,
( relation(function_inverse(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_158,c_112]) ).
cnf(c_354,negated_conjecture,
relation(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_113,c_7174]) ).
cnf(c_7175,plain,
( apply(relation_composition(function_inverse(sK0),A),B) = apply(A,apply(function_inverse(sK0),B))
| ~ in(B,relation_rng(sK0))
| ~ function(A)
| ~ relation(A)
| ~ function(function_inverse(sK0))
| ~ relation(function_inverse(sK0)) ),
inference(paramod,[status(thm)],[c_193,c_120]) ).
cnf(c_7176,plain,
( apply(relation_composition(function_inverse(sK0),A),B) = apply(A,apply(function_inverse(sK0),B))
| ~ in(B,relation_rng(sK0))
| ~ function(A)
| ~ relation(A)
| ~ function(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_354,c_7175]) ).
cnf(c_366,plain,
( apply(relation_composition(function_inverse(sK0),A),B) = apply(A,apply(function_inverse(sK0),B))
| ~ in(B,relation_rng(sK0))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_351,c_7176]) ).
cnf(c_7177,negated_conjecture,
( apply(sK0,B) = A
| apply(function_inverse(sK0),A) != B
| ~ in(A,relation_rng(sK0))
| function_inverse(sK0) != function_inverse(sK0)
| ~ function(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_201,c_354]) ).
cnf(c_7178,negated_conjecture,
( apply(sK0,B) = A
| apply(function_inverse(sK0),A) != B
| ~ in(A,relation_rng(sK0))
| function_inverse(sK0) != function_inverse(sK0) ),
inference(resolve,[status(thm)],[c_7177,c_351]) ).
cnf(c_7179,plain,
( apply(sK0,B) = A
| apply(function_inverse(sK0),A) != B
| ~ in(A,relation_rng(sK0)) ),
inference(xxres,[status(thm)],[c_7178]) ).
cnf(c_7180,negated_conjecture,
( apply(sK0,A) = sK1
| apply(function_inverse(sK0),sK1) != A ),
inference(resolve,[status(thm)],[c_7179,c_111]) ).
cnf(c_615,plain,
apply(sK0,apply(function_inverse(sK0),sK1)) = sK1,
inference(xxres,[status(thm)],[c_7180]) ).
cnf(c_7181,negated_conjecture,
( apply(relation_composition(function_inverse(sK0),sK0),sK1) != sK1
| sK1 != sK1 ),
inference(paramod,[status(thm)],[c_615,c_110]) ).
cnf(c_648,negated_conjecture,
apply(relation_composition(function_inverse(sK0),sK0),sK1) != sK1,
inference(copy,[status(thm)],[c_7181]) ).
cnf(c_7182,negated_conjecture,
( apply(relation_composition(function_inverse(sK0),sK0),A) = apply(sK0,apply(function_inverse(sK0),A))
| ~ in(A,relation_rng(sK0))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_366,c_113]) ).
cnf(c_7183,negated_conjecture,
( apply(relation_composition(function_inverse(sK0),sK0),A) = apply(sK0,apply(function_inverse(sK0),A))
| ~ in(A,relation_rng(sK0)) ),
inference(resolve,[status(thm)],[c_7182,c_112]) ).
cnf(c_7184,negated_conjecture,
apply(relation_composition(function_inverse(sK0),sK0),sK1) = apply(sK0,apply(function_inverse(sK0),sK1)),
inference(resolve,[status(thm)],[c_7183,c_111]) ).
cnf(c_7185,negated_conjecture,
apply(relation_composition(function_inverse(sK0),sK0),sK1) = sK1,
inference(paramod,[status(thm)],[c_615,c_7184]) ).
cnf(c_7170,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_648,c_7185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU220+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:53:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3251132 was started by sandbox on n008,
% 0.09/0.36 % Sat Sep 26 08:53:54 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 25.96/3.83
% 25.96/3.83 % SZS status Theorem for theBenchmark
% 25.96/3.83
% 25.96/3.83 % Proof 1 at 3.13 (+ 0.30) seconds.
% 25.96/3.83 % Length of proof is 26.
% 25.96/3.83 % Level of proof is 6.
% 25.96/3.83 % Maximum clause weight is 46.000.
% 25.96/3.83 % Given clauses 407.
% 25.96/3.83
% 25.96/3.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------