%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU041+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 : n002.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 08:44:56 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 48 ( 23 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 47 ( 18 ~; 11 |; 10 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t102_relat_1,axiom,
! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> relation_dom_restriction(relation_dom_restriction(C,A),B) = relation_dom_restriction(C,A) ) ),
file('theBenchmark.p',t102_relat_1) ).
fof(t103_relat_1,axiom,
! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> relation_dom_restriction(relation_dom_restriction(C,B),A) = relation_dom_restriction(C,A) ) ),
file('theBenchmark.p',t103_relat_1) ).
fof(t82_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( subset(A,B)
=> ( relation_dom_restriction(relation_dom_restriction(C,B),A) = relation_dom_restriction(C,A)
& relation_dom_restriction(relation_dom_restriction(C,A),B) = relation_dom_restriction(C,A) ) ) ),
file('theBenchmark.p',t82_funct_1) ).
fof(t82_funct_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( subset(A,B)
=> ( relation_dom_restriction(relation_dom_restriction(C,B),A) = relation_dom_restriction(C,A)
& relation_dom_restriction(relation_dom_restriction(C,A),B) = relation_dom_restriction(C,A) ) ) ),
inference(assume_negation,[status(cth)],[t82_funct_1]) ).
cnf(c_34,plain,
( relation_dom_restriction(relation_dom_restriction(A,C),B) = relation_dom_restriction(A,B)
| ~ subset(B,C)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t103_relat_1]) ).
fof(nnf_33,plain,
? [A,B,C] :
( ( relation_dom_restriction(relation_dom_restriction(C,B),A) != relation_dom_restriction(C,A)
| relation_dom_restriction(relation_dom_restriction(C,A),B) != relation_dom_restriction(C,A) )
& subset(A,B)
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t82_funct_1_neg]) ).
fof(sk_t82_funct_1_neg,plain,
( ( relation_dom_restriction(relation_dom_restriction(sK2,sK1),sK0) != relation_dom_restriction(sK2,sK0)
| relation_dom_restriction(relation_dom_restriction(sK2,sK0),sK1) != relation_dom_restriction(sK2,sK0) )
& subset(sK0,sK1)
& function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_33]) ).
cnf(c_35,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t82_funct_1_neg]) ).
cnf(c_36,plain,
( relation_dom_restriction(relation_dom_restriction(A,B),C) = relation_dom_restriction(A,B)
| ~ subset(B,C)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t102_relat_1]) ).
cnf(c_45,negated_conjecture,
( relation_dom_restriction(relation_dom_restriction(A,sK0),sK1) = relation_dom_restriction(A,sK0)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_36,c_35]) ).
cnf(c_46,negated_conjecture,
( relation_dom_restriction(relation_dom_restriction(A,sK1),sK0) = relation_dom_restriction(A,sK0)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_34,c_35]) ).
cnf(c_85,negated_conjecture,
relation(sK2),
inference(split_conjunct,[status(thm)],[sk_t82_funct_1_neg]) ).
cnf(c_87,negated_conjecture,
( relation_dom_restriction(relation_dom_restriction(sK2,sK1),sK0) != relation_dom_restriction(sK2,sK0)
| relation_dom_restriction(relation_dom_restriction(sK2,sK0),sK1) != relation_dom_restriction(sK2,sK0) ),
inference(split_conjunct,[status(thm)],[sk_t82_funct_1_neg]) ).
cnf(c_182,plain,
relation_dom_restriction(relation_dom_restriction(sK2,sK1),sK0) = relation_dom_restriction(sK2,sK0),
inference(resolve,[status(thm)],[c_85,c_46]) ).
cnf(c_183,plain,
relation_dom_restriction(relation_dom_restriction(sK2,sK0),sK1) = relation_dom_restriction(sK2,sK0),
inference(resolve,[status(thm)],[c_85,c_45]) ).
cnf(c_188,negated_conjecture,
( relation_dom_restriction(relation_dom_restriction(sK2,sK1),sK0) != relation_dom_restriction(sK2,sK0)
| relation_dom_restriction(sK2,sK0) != relation_dom_restriction(sK2,sK0) ),
inference(paramod,[status(thm)],[c_183,c_87]) ).
cnf(c_189,negated_conjecture,
( relation_dom_restriction(sK2,sK0) != relation_dom_restriction(sK2,sK0)
| relation_dom_restriction(sK2,sK0) != relation_dom_restriction(sK2,sK0) ),
inference(paramod,[status(thm)],[c_182,c_188]) ).
cnf(c_190,negated_conjecture,
relation_dom_restriction(sK2,sK0) != relation_dom_restriction(sK2,sK0),
inference(copy,[status(thm)],[c_189]) ).
cnf(c_187,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU041+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n002.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 08:34:37 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 1266117 was started by sandbox2 on n002,
% 0.17/0.45 % Sat Sep 26 08:34:37 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.48
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48
% 0.17/0.48 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.48 % Length of proof is 13.
% 0.17/0.48 % Level of proof is 4.
% 0.17/0.48 % Maximum clause weight is 43.000.
% 0.17/0.48 % Given clauses 43.
% 0.17/0.48
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------