%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU353+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:45:53 AM UTC 2026
% Result : Theorem 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 17 unt; 0 def)
% Number of atoms : 110 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 106 ( 42 ~; 38 |; 15 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-4 aty)
% Number of variables : 52 ( 0 sgn 19 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d11_grcat_1,axiom,
! [A] :
( one_sorted_str(A)
=> identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)) ),
file('theBenchmark.p',d11_grcat_1) ).
fof(dt_k7_grcat_1,axiom,
! [A] :
( one_sorted_str(A)
=> ( relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A))
& quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A))
& function(identity_on_carrier(A)) ) ),
file('theBenchmark.p',dt_k7_grcat_1) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(the_carrier(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(redefinition_k6_partfun1,axiom,
! [A] : identity_as_relation_of(A) = identity_relation(A),
file('theBenchmark.p',redefinition_k6_partfun1) ).
fof(redefinition_k8_funct_2,axiom,
! [A,B,C,D] :
( ( element(D,A)
& relation_of2(C,A,B)
& quasi_total(C,A,B)
& function(C)
& ~ empty(A) )
=> apply_as_element(A,B,C,D) = apply(C,D) ),
file('theBenchmark.p',redefinition_k8_funct_2) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t35_funct_1,axiom,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('theBenchmark.p',t35_funct_1) ).
fof(t91_tmap_1,conjecture,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B) = B ) ),
file('theBenchmark.p',t91_tmap_1) ).
fof(t91_tmap_1_neg,negated_conjecture,
~ ! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B) = B ) ),
inference(assume_negation,[status(cth)],[t91_tmap_1]) ).
cnf(c_57,plain,
( function(identity_on_carrier(A))
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[dt_k7_grcat_1]) ).
cnf(c_74,plain,
( apply(B,D) = apply_as_element(A,C,B,D)
| ~ element(D,A)
| ~ relation_of2(B,A,C)
| ~ quasi_total(B,A,C)
| ~ function(B)
| empty(A) ),
inference(clausify,[status(thm)],[redefinition_k8_funct_2]) ).
cnf(c_85,plain,
( relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A))
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[dt_k7_grcat_1]) ).
cnf(c_86,plain,
( quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A))
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[dt_k7_grcat_1]) ).
cnf(c_87,plain,
( identity_as_relation_of(the_carrier(A)) = identity_on_carrier(A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d11_grcat_1]) ).
cnf(c_88,plain,
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[fc1_struct_0]) ).
fof(nnf_56,plain,
? [A] :
( ? [B] :
( apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B) != B
& element(B,the_carrier(A)) )
& one_sorted_str(A)
& ~ empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t91_tmap_1_neg]) ).
fof(sk_t91_tmap_1_neg,plain,
( apply_as_element(the_carrier(sK0),the_carrier(sK0),identity_on_carrier(sK0),sK1) != sK1
& element(sK1,the_carrier(sK0))
& one_sorted_str(sK0)
& ~ empty_carrier(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_56]) ).
cnf(c_92,negated_conjecture,
one_sorted_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t91_tmap_1_neg]) ).
cnf(c_104,plain,
( ~ one_sorted_str(B)
| apply(identity_on_carrier(B),D) = apply_as_element(A,C,identity_on_carrier(B),D)
| ~ element(D,A)
| ~ relation_of2(identity_on_carrier(B),A,C)
| ~ quasi_total(identity_on_carrier(B),A,C)
| empty(A) ),
inference(resolve,[status(thm)],[c_74,c_57]) ).
cnf(c_105,plain,
( relation_of2(A,B,C)
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_109,negated_conjecture,
relation_of2_as_subset(identity_on_carrier(sK0),the_carrier(sK0),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_92,c_85]) ).
cnf(c_125,negated_conjecture,
relation_of2(identity_on_carrier(sK0),the_carrier(sK0),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_105,c_109]) ).
cnf(c_167,plain,
identity_relation(A) = identity_as_relation_of(A),
inference(clausify,[status(thm)],[redefinition_k6_partfun1]) ).
cnf(c_169,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_170,plain,
( apply(identity_relation(B),A) = A
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t35_funct_1]) ).
cnf(c_171,plain,
( apply(identity_as_relation_of(B),A) = A
| ~ in(A,B) ),
inference(paramod,[status(thm)],[c_167,c_170]) ).
cnf(c_177,negated_conjecture,
~ empty_carrier(sK0),
inference(split_conjunct,[status(thm)],[sk_t91_tmap_1_neg]) ).
cnf(c_178,negated_conjecture,
element(sK1,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t91_tmap_1_neg]) ).
cnf(c_179,negated_conjecture,
apply_as_element(the_carrier(sK0),the_carrier(sK0),identity_on_carrier(sK0),sK1) != sK1,
inference(split_conjunct,[status(thm)],[sk_t91_tmap_1_neg]) ).
cnf(c_272,negated_conjecture,
( ~ empty(the_carrier(sK0))
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_92,c_88]) ).
cnf(c_273,negated_conjecture,
~ empty(the_carrier(sK0)),
inference(resolve,[status(thm)],[c_177,c_272]) ).
cnf(c_274,negated_conjecture,
quasi_total(identity_on_carrier(sK0),the_carrier(sK0),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_92,c_86]) ).
cnf(c_275,negated_conjecture,
identity_as_relation_of(the_carrier(sK0)) = identity_on_carrier(sK0),
inference(resolve,[status(thm)],[c_92,c_87]) ).
cnf(c_309,negated_conjecture,
( apply(identity_on_carrier(sK0),C) = apply_as_element(A,B,identity_on_carrier(sK0),C)
| ~ element(C,A)
| ~ relation_of2(identity_on_carrier(sK0),A,B)
| ~ quasi_total(identity_on_carrier(sK0),A,B)
| empty(A) ),
inference(resolve,[status(thm)],[c_104,c_92]) ).
cnf(c_310,negated_conjecture,
( apply_as_element(A,B,identity_on_carrier(sK0),C) = apply(identity_on_carrier(sK0),C)
| ~ element(C,A)
| ~ relation_of2(identity_on_carrier(sK0),A,B)
| ~ quasi_total(identity_on_carrier(sK0),A,B)
| empty(A) ),
inference(copy,[status(thm)],[c_309]) ).
cnf(c_521,negated_conjecture,
( in(sK1,the_carrier(sK0))
| empty(the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_178,c_169]) ).
cnf(c_370,negated_conjecture,
in(sK1,the_carrier(sK0)),
inference(resolve,[status(thm)],[c_273,c_521]) ).
cnf(c_522,negated_conjecture,
( apply_as_element(the_carrier(sK0),the_carrier(sK0),identity_on_carrier(sK0),A) = apply(identity_on_carrier(sK0),A)
| ~ element(A,the_carrier(sK0))
| ~ relation_of2(identity_on_carrier(sK0),the_carrier(sK0),the_carrier(sK0))
| empty(the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_310,c_274]) ).
cnf(c_523,negated_conjecture,
( apply_as_element(the_carrier(sK0),the_carrier(sK0),identity_on_carrier(sK0),A) = apply(identity_on_carrier(sK0),A)
| ~ element(A,the_carrier(sK0))
| empty(the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_522,c_125]) ).
cnf(c_524,negated_conjecture,
( apply_as_element(the_carrier(sK0),the_carrier(sK0),identity_on_carrier(sK0),sK1) = apply(identity_on_carrier(sK0),sK1)
| empty(the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_523,c_178]) ).
cnf(c_460,negated_conjecture,
apply_as_element(the_carrier(sK0),the_carrier(sK0),identity_on_carrier(sK0),sK1) = apply(identity_on_carrier(sK0),sK1),
inference(resolve,[status(thm)],[c_273,c_524]) ).
cnf(c_463,negated_conjecture,
apply(identity_on_carrier(sK0),sK1) != sK1,
inference(paramod,[status(thm)],[c_460,c_179]) ).
cnf(c_525,plain,
apply(identity_as_relation_of(the_carrier(sK0)),sK1) = sK1,
inference(resolve,[status(thm)],[c_370,c_171]) ).
cnf(c_526,plain,
apply(identity_on_carrier(sK0),sK1) = sK1,
inference(paramod,[status(thm)],[c_275,c_525]) ).
cnf(c_520,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_463,c_526]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU353+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 09:13:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 364355 was started by sandbox2 on n017,
% 0.11/0.37 % Sat Sep 26 09:13:19 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.39
% 0.14/0.39 % From the command line: assign(max_seconds, 300).
% 0.14/0.47
% 0.14/0.47 % SZS status Theorem for theBenchmark
% 0.14/0.47
% 0.14/0.47 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.14/0.47 % Length of proof is 37.
% 0.14/0.47 % Level of proof is 7.
% 0.14/0.47 % Maximum clause weight is 41.000.
% 0.14/0.47 % Given clauses 189.
% 0.14/0.47
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------