%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU025+1 : 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 : n017.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 2.24s 1.08s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 12 unt; 0 def)
% Number of atoms : 103 ( 37 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 105 ( 42 ~; 36 |; 14 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 21 ( 1 sgn 10 !; 1 ?)
% 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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t46_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_rng(A),relation_dom(B))
=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ),
file('theBenchmark.p',t46_relat_1) ).
fof(t47_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_dom(A),relation_rng(B))
=> relation_rng(relation_composition(B,A)) = relation_rng(A) ) ) ),
file('theBenchmark.p',t47_relat_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(t58_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_rng(relation_composition(A,function_inverse(A))) = relation_dom(A)
& relation_dom(relation_composition(A,function_inverse(A))) = relation_dom(A) ) ) ),
file('theBenchmark.p',t58_funct_1) ).
fof(t58_funct_1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_rng(relation_composition(A,function_inverse(A))) = relation_dom(A)
& relation_dom(relation_composition(A,function_inverse(A))) = relation_dom(A) ) ) ),
inference(assume_negation,[status(cth)],[t58_funct_1]) ).
cnf(c_41,plain,
( relation_rng(A) = relation_dom(function_inverse(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t55_funct_1]) ).
cnf(c_44,plain,
( relation_rng(function_inverse(A)) = relation_dom(A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t55_funct_1]) ).
fof(nnf_40,plain,
? [A] :
( ( relation_rng(relation_composition(A,function_inverse(A))) != relation_dom(A)
| relation_dom(relation_composition(A,function_inverse(A))) != relation_dom(A) )
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t58_funct_1_neg]) ).
fof(sk_t58_funct_1_neg,plain,
( ( relation_rng(relation_composition(sK0,function_inverse(sK0))) != relation_dom(sK0)
| relation_dom(relation_composition(sK0,function_inverse(sK0))) != relation_dom(sK0) )
& one_to_one(sK0)
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_40]) ).
cnf(c_45,negated_conjecture,
one_to_one(sK0),
inference(split_conjunct,[status(thm)],[sk_t58_funct_1_neg]) ).
cnf(c_49,plain,
( relation(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_85,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_90,plain,
( relation_dom(relation_composition(A,B)) = relation_dom(A)
| ~ subset(relation_rng(A),relation_dom(B))
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t46_relat_1]) ).
cnf(c_91,plain,
( relation_rng(relation_composition(B,A)) = relation_rng(A)
| ~ subset(relation_dom(A),relation_rng(B))
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t47_relat_1]) ).
cnf(c_97,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t58_funct_1_neg]) ).
cnf(c_98,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t58_funct_1_neg]) ).
cnf(c_99,negated_conjecture,
( relation_rng(relation_composition(sK0,function_inverse(sK0))) != relation_dom(sK0)
| relation_dom(relation_composition(sK0,function_inverse(sK0))) != relation_dom(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t58_funct_1_neg]) ).
cnf(c_108,negated_conjecture,
( relation_rng(function_inverse(sK0)) = relation_dom(sK0)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_45,c_44]) ).
cnf(c_3130,negated_conjecture,
( relation_rng(function_inverse(sK0)) = relation_dom(sK0)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_97,c_108]) ).
cnf(c_109,negated_conjecture,
relation_rng(function_inverse(sK0)) = relation_dom(sK0),
inference(resolve,[status(thm)],[c_98,c_3130]) ).
cnf(c_110,negated_conjecture,
( relation_rng(sK0) = relation_dom(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_45,c_41]) ).
cnf(c_3131,negated_conjecture,
( relation_dom(function_inverse(sK0)) = relation_rng(sK0)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(copy,[status(thm)],[c_110]) ).
cnf(c_3132,negated_conjecture,
( relation_dom(function_inverse(sK0)) = relation_rng(sK0)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_97,c_3131]) ).
cnf(c_111,negated_conjecture,
relation_dom(function_inverse(sK0)) = relation_rng(sK0),
inference(resolve,[status(thm)],[c_98,c_3132]) ).
cnf(c_303,plain,
( relation_rng(relation_composition(sK0,A)) = relation_rng(A)
| ~ subset(relation_dom(A),relation_rng(sK0))
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_97,c_91]) ).
cnf(c_306,plain,
( relation_dom(relation_composition(sK0,A)) = relation_dom(sK0)
| ~ subset(relation_rng(sK0),relation_dom(A))
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_97,c_90]) ).
cnf(c_3133,negated_conjecture,
( relation(function_inverse(sK0))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_97,c_49]) ).
cnf(c_318,negated_conjecture,
relation(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_98,c_3133]) ).
cnf(c_3134,plain,
( relation_rng(relation_composition(sK0,function_inverse(sK0))) = relation_rng(function_inverse(sK0))
| ~ subset(relation_dom(function_inverse(sK0)),relation_rng(sK0)) ),
inference(resolve,[status(thm)],[c_303,c_318]) ).
cnf(c_3135,plain,
( relation_rng(relation_composition(sK0,function_inverse(sK0))) = relation_rng(function_inverse(sK0))
| ~ subset(relation_rng(sK0),relation_rng(sK0)) ),
inference(paramod,[status(thm)],[c_111,c_3134]) ).
cnf(c_3136,plain,
( relation_rng(relation_composition(sK0,function_inverse(sK0))) = relation_dom(sK0)
| ~ subset(relation_rng(sK0),relation_rng(sK0)) ),
inference(paramod,[status(thm)],[c_109,c_3135]) ).
cnf(c_3030,plain,
relation_rng(relation_composition(sK0,function_inverse(sK0))) = relation_dom(sK0),
inference(resolve,[status(thm)],[c_85,c_3136]) ).
cnf(c_3137,negated_conjecture,
( relation_dom(sK0) != relation_dom(sK0)
| relation_dom(relation_composition(sK0,function_inverse(sK0))) != relation_dom(sK0) ),
inference(paramod,[status(thm)],[c_3030,c_99]) ).
cnf(c_3033,negated_conjecture,
relation_dom(relation_composition(sK0,function_inverse(sK0))) != relation_dom(sK0),
inference(copy,[status(thm)],[c_3137]) ).
cnf(c_3138,plain,
( relation_dom(relation_composition(sK0,function_inverse(sK0))) = relation_dom(sK0)
| ~ subset(relation_rng(sK0),relation_dom(function_inverse(sK0))) ),
inference(resolve,[status(thm)],[c_306,c_318]) ).
cnf(c_3139,plain,
( relation_dom(relation_composition(sK0,function_inverse(sK0))) = relation_dom(sK0)
| ~ subset(relation_rng(sK0),relation_rng(sK0)) ),
inference(paramod,[status(thm)],[c_111,c_3138]) ).
cnf(c_3140,plain,
relation_dom(relation_composition(sK0,function_inverse(sK0))) = relation_dom(sK0),
inference(resolve,[status(thm)],[c_85,c_3139]) ).
cnf(c_3129,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_3033,c_3140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU025+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.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 08:26:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 273168 was started by sandbox on n017,
% 0.09/0.37 % Sat Sep 26 08:26:04 2026
% 0.09/0.37 % 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).
% 2.24/1.08
% 2.24/1.08 % SZS status Theorem for theBenchmark
% 2.24/1.08
% 2.24/1.08 % Proof 1 at 0.25 (+ 0.12) seconds.
% 2.24/1.08 % Length of proof is 26.
% 2.24/1.08 % Level of proof is 6.
% 2.24/1.08 % Maximum clause weight is 36.000.
% 2.24/1.08 % Given clauses 380.
% 2.24/1.08
% 2.24/1.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------