%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU020+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 : n012.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 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 100 ( 15 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 109 ( 41 ~; 36 |; 22 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 1 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t27_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( relation_dom(relation_composition(B,A)) = relation_dom(B)
=> subset(relation_rng(B),relation_dom(A)) ) ) ),
file('theBenchmark.p',t27_funct_1) ).
fof(t47_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( subset(relation_rng(B),relation_dom(A))
& one_to_one(relation_composition(B,A)) )
=> one_to_one(B) ) ) ),
file('theBenchmark.p',t47_funct_1) ).
fof(t52_funct_1,axiom,
! [A] : one_to_one(identity_relation(A)),
file('theBenchmark.p',t52_funct_1) ).
fof(t71_relat_1,axiom,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('theBenchmark.p',t71_relat_1) ).
fof(t53_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( ? [B] :
( relation_composition(A,B) = identity_relation(relation_dom(A))
& function(B)
& relation(B) )
=> one_to_one(A) ) ),
file('theBenchmark.p',t53_funct_1) ).
fof(t53_funct_1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( ? [B] :
( relation_composition(A,B) = identity_relation(relation_dom(A))
& function(B)
& relation(B) )
=> one_to_one(A) ) ),
inference(assume_negation,[status(cth)],[t53_funct_1]) ).
fof(nnf_39,plain,
? [A] :
( ~ one_to_one(A)
& ? [B] :
( identity_relation(relation_dom(A)) = relation_composition(A,B)
& function(B)
& relation(B) )
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t53_funct_1_neg]) ).
fof(sk_t53_funct_1_neg,plain,
( ~ one_to_one(sK0)
& identity_relation(relation_dom(sK0)) = relation_composition(sK0,sK1)
& function(sK1)
& relation(sK1)
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_39]) ).
cnf(c_40,negated_conjecture,
~ one_to_one(sK0),
inference(split_conjunct,[status(thm)],[sk_t53_funct_1_neg]) ).
cnf(c_41,negated_conjecture,
identity_relation(relation_dom(sK0)) = relation_composition(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t53_funct_1_neg]) ).
cnf(c_42,negated_conjecture,
function(sK1),
inference(split_conjunct,[status(thm)],[sk_t53_funct_1_neg]) ).
cnf(c_43,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t53_funct_1_neg]) ).
cnf(c_44,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t53_funct_1_neg]) ).
cnf(c_45,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t53_funct_1_neg]) ).
cnf(c_49,plain,
relation_dom(identity_relation(A)) = A,
inference(clausify,[status(thm)],[t71_relat_1]) ).
cnf(c_52,plain,
one_to_one(identity_relation(A)),
inference(clausify,[status(thm)],[t52_funct_1]) ).
cnf(c_54,plain,
( one_to_one(B)
| ~ subset(relation_rng(B),relation_dom(A))
| ~ one_to_one(relation_composition(B,A))
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t47_funct_1]) ).
cnf(c_58,plain,
( subset(relation_rng(B),relation_dom(A))
| relation_dom(relation_composition(B,A)) != relation_dom(B)
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t27_funct_1]) ).
cnf(c_103,plain,
relation_dom(relation_composition(sK0,sK1)) = relation_dom(sK0),
inference(paramod,[status(thm)],[c_41,c_49]) ).
cnf(c_104,plain,
one_to_one(relation_composition(sK0,sK1)),
inference(paramod,[status(thm)],[c_41,c_52]) ).
cnf(c_270,negated_conjecture,
( subset(relation_rng(A),relation_dom(sK1))
| relation_dom(relation_composition(A,sK1)) != relation_dom(A)
| ~ function(A)
| ~ relation(A)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_58,c_42]) ).
cnf(c_106,negated_conjecture,
( subset(relation_rng(A),relation_dom(sK1))
| relation_dom(relation_composition(A,sK1)) != relation_dom(A)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_43,c_270]) ).
cnf(c_271,negated_conjecture,
( one_to_one(A)
| ~ subset(relation_rng(A),relation_dom(sK1))
| ~ one_to_one(relation_composition(A,sK1))
| ~ function(A)
| ~ relation(A)
| ~ function(sK1) ),
inference(resolve,[status(thm)],[c_54,c_43]) ).
cnf(c_272,negated_conjecture,
( one_to_one(A)
| ~ subset(relation_rng(A),relation_dom(sK1))
| ~ one_to_one(relation_composition(A,sK1))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_271,c_42]) ).
cnf(c_273,negated_conjecture,
( one_to_one(sK0)
| ~ subset(relation_rng(sK0),relation_dom(sK1))
| ~ one_to_one(relation_composition(sK0,sK1))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_272,c_45]) ).
cnf(c_274,negated_conjecture,
( one_to_one(sK0)
| ~ subset(relation_rng(sK0),relation_dom(sK1))
| ~ one_to_one(relation_composition(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_273,c_44]) ).
cnf(c_275,negated_conjecture,
( one_to_one(sK0)
| ~ subset(relation_rng(sK0),relation_dom(sK1)) ),
inference(resolve,[status(thm)],[c_274,c_104]) ).
cnf(c_237,negated_conjecture,
~ subset(relation_rng(sK0),relation_dom(sK1)),
inference(resolve,[status(thm)],[c_275,c_40]) ).
cnf(c_276,negated_conjecture,
( subset(relation_rng(sK0),relation_dom(sK1))
| relation_dom(relation_composition(sK0,sK1)) != relation_dom(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_106,c_44]) ).
cnf(c_277,negated_conjecture,
( subset(relation_rng(sK0),relation_dom(sK1))
| relation_dom(relation_composition(sK0,sK1)) != relation_dom(sK0) ),
inference(resolve,[status(thm)],[c_45,c_276]) ).
cnf(c_278,negated_conjecture,
subset(relation_rng(sK0),relation_dom(sK1)),
inference(resolve,[status(thm)],[c_103,c_277]) ).
cnf(c_269,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_237,c_278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU020+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:30:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 148713 was started by sandbox2 on n012,
% 0.08/0.35 % Sat Sep 26 08:30:36 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.39
% 0.12/0.39 % SZS status Theorem for theBenchmark
% 0.12/0.39
% 0.12/0.39 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.12/0.39 % Length of proof is 20.
% 0.12/0.39 % Level of proof is 4.
% 0.12/0.39 % Maximum clause weight is 35.000.
% 0.12/0.39 % Given clauses 75.
% 0.12/0.39
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------