%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU010+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 : n016.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 08:44:53 AM UTC 2026
% Result : Theorem 0.09s 15.48s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 43 ( 21 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 40 ( 16 ~; 10 |; 8 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 16 ( 1 sgn 8 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t77_relat_1,axiom,
! [A,B] :
( relation(B)
=> ( subset(relation_dom(B),A)
=> relation_composition(identity_relation(A),B) = B ) ),
file('theBenchmark.p',t77_relat_1) ).
fof(t79_relat_1,axiom,
! [A,B] :
( relation(B)
=> ( subset(relation_rng(B),A)
=> relation_composition(B,identity_relation(A)) = B ) ),
file('theBenchmark.p',t79_relat_1) ).
fof(t42_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( relation_composition(A,identity_relation(relation_rng(A))) = A
& relation_composition(identity_relation(relation_dom(A)),A) = A ) ),
file('theBenchmark.p',t42_funct_1) ).
fof(t42_funct_1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( relation_composition(A,identity_relation(relation_rng(A))) = A
& relation_composition(identity_relation(relation_dom(A)),A) = A ) ),
inference(assume_negation,[status(cth)],[t42_funct_1]) ).
fof(nnf_37,plain,
? [A] :
( ( relation_composition(A,identity_relation(relation_rng(A))) != A
| relation_composition(identity_relation(relation_dom(A)),A) != A )
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t42_funct_1_neg]) ).
fof(sk_t42_funct_1_neg,plain,
( ( relation_composition(sK0,identity_relation(relation_rng(sK0))) != sK0
| relation_composition(identity_relation(relation_dom(sK0)),sK0) != sK0 )
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_37]) ).
cnf(c_38,negated_conjecture,
( relation_composition(sK0,identity_relation(relation_rng(sK0))) != sK0
| relation_composition(identity_relation(relation_dom(sK0)),sK0) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_t42_funct_1_neg]) ).
cnf(c_40,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t42_funct_1_neg]) ).
cnf(c_41,plain,
( relation_composition(A,identity_relation(B)) = A
| ~ subset(relation_rng(A),B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t79_relat_1]) ).
cnf(c_42,plain,
( relation_composition(identity_relation(B),A) = A
| ~ subset(relation_dom(A),B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t77_relat_1]) ).
cnf(c_63,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_92,plain,
( relation_composition(sK0,identity_relation(A)) = sK0
| ~ subset(relation_rng(sK0),A) ),
inference(resolve,[status(thm)],[c_41,c_40]) ).
cnf(c_93,plain,
( relation_composition(identity_relation(A),sK0) = sK0
| ~ subset(relation_dom(sK0),A) ),
inference(resolve,[status(thm)],[c_42,c_40]) ).
cnf(c_222,plain,
relation_composition(sK0,identity_relation(relation_rng(sK0))) = sK0,
inference(resolve,[status(thm)],[c_92,c_63]) ).
cnf(c_225,negated_conjecture,
( sK0 != sK0
| relation_composition(identity_relation(relation_dom(sK0)),sK0) != sK0 ),
inference(paramod,[status(thm)],[c_222,c_38]) ).
cnf(c_223,negated_conjecture,
relation_composition(identity_relation(relation_dom(sK0)),sK0) != sK0,
inference(copy,[status(thm)],[c_225]) ).
cnf(c_226,plain,
relation_composition(identity_relation(relation_dom(sK0)),sK0) = sK0,
inference(resolve,[status(thm)],[c_93,c_63]) ).
cnf(c_224,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_223,c_226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU010+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/15.45 % CPULimit : 300
% 0.09/15.45 % WCLimit : 300
% 0.09/15.45 % DateTime : Sat Sep 26 08:30:50 UTC 2026
% 0.09/15.45 % CPUTime :
% 0.09/15.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/15.45 % Process 856461 was started by sandbox2 on n019,
% 0.09/15.45 % Sat Sep 26 08:30:50 2026
% 0.09/15.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/15.46
% 0.09/15.46 % From the command line: assign(max_seconds, 300).
% 0.09/15.48
% 0.09/15.48 % SZS status Theorem for theBenchmark
% 0.09/15.48
% 0.09/15.48 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/15.48 % Length of proof is 14.
% 0.09/15.48 % Level of proof is 5.
% 0.09/15.48 % Maximum clause weight is 34.000.
% 0.09/15.48 % Given clauses 54.
% 0.09/15.48
% 0.09/15.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------