%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU353+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n018.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 : Fri Sep 25 02:57:01 PM UTC 2026
% Result : Theorem 3.62s 6.28s
% Output : CNFRefutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 75 ( 21 unt; 0 def)
% Number of atoms : 181 ( 39 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 188 ( 82 ~; 74 |; 20 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 93 ( 0 sgn 89 !; 4 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( one_sorted_str(X0)
=> identity_on_carrier(X0) = identity_as_relation_of(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_grcat_1) ).
fof(f17,axiom,
! [X0] :
( one_sorted_str(X0)
=> ( relation_of2_as_subset(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
& quasi_total(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
& function(identity_on_carrier(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_grcat_1) ).
fof(f28,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f44,axiom,
! [X0] : identity_as_relation_of(X0) = identity_relation(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
fof(f45,axiom,
! [X0,X1,X2,X3] :
( ( element(X3,X0)
& relation_of2(X2,X0,X1)
& quasi_total(X2,X0,X1)
& function(X2)
& ~ empty(X0) )
=> apply_as_element(X0,X1,X2,X3) = apply(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
fof(f46,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f49,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f50,axiom,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f57,conjecture,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_tmap_1) ).
fof(f58,negated_conjecture,
~ ! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> relation_of2(X2,X0,X1) ),
inference(unused_predicate_definition_removal,[],[f46]) ).
fof(f62,plain,
? [X0] :
( one_sorted_str(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) != X1 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f63,plain,
? [X0] :
( one_sorted_str(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& apply_as_element(the_carrier(X0),the_carrier(X0),identity_on_carrier(X0),X1) != X1 ) ),
inference(flattening,[],[f62]) ).
fof(f65,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ( relation_of2_as_subset(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
& quasi_total(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
& function(identity_on_carrier(X0)) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f66,plain,
! [X0] :
( ~ one_sorted_str(X0)
| identity_on_carrier(X0) = identity_as_relation_of(the_carrier(X0)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f69,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f70,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( ~ element(X3,X0)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2)
| empty(X0)
| apply_as_element(X0,X1,X2,X3) = apply(X2,X3) ),
inference(ennf_transformation,[],[f45]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( ~ element(X3,X0)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2)
| empty(X0)
| apply_as_element(X0,X1,X2,X3) = apply(X2,X3) ),
inference(flattening,[],[f71]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f80,plain,
! [X0,X1] :
( ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(ennf_transformation,[],[f50]) ).
fof(f90,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f91,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f90]) ).
fof(f100,plain,
( one_sorted_str(sK0)
& ~ empty_carrier(sK0)
& element(sK1,the_carrier(sK0))
& sK1 != apply_as_element(the_carrier(sK0),the_carrier(sK0),identity_on_carrier(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f63]) ).
fof(f116,plain,
one_sorted_str(sK0),
inference(cnf_transformation,[],[f100]) ).
fof(f117,plain,
~ empty_carrier(sK0),
inference(cnf_transformation,[],[f100]) ).
fof(f118,plain,
element(sK1,the_carrier(sK0)),
inference(cnf_transformation,[],[f100]) ).
fof(f119,plain,
sK1 != apply_as_element(the_carrier(sK0),the_carrier(sK0),identity_on_carrier(sK0),sK1),
inference(cnf_transformation,[],[f100]) ).
fof(f121,plain,
! [X0] :
( ~ one_sorted_str(X0)
| relation_of2_as_subset(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f122,plain,
! [X0] :
( ~ one_sorted_str(X0)
| quasi_total(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f123,plain,
! [X0] :
( ~ one_sorted_str(X0)
| function(identity_on_carrier(X0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f124,plain,
! [X0] :
( ~ one_sorted_str(X0)
| identity_on_carrier(X0) = identity_as_relation_of(the_carrier(X0)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f127,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( ~ element(X3,X0)
| ~ relation_of2(X2,X0,X1)
| ~ quasi_total(X2,X0,X1)
| ~ function(X2)
| empty(X0)
| apply_as_element(X0,X1,X2,X3) = apply(X2,X3) ),
inference(cnf_transformation,[],[f72]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f142,plain,
! [X0] : identity_as_relation_of(X0) = identity_relation(X0),
inference(cnf_transformation,[],[f44]) ).
fof(f153,plain,
! [X0,X1] :
( ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(cnf_transformation,[],[f80]) ).
fof(f173,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f207,plain,
! [X0] :
( ~ one_sorted_str(X0)
| identity_on_carrier(X0) = identity_relation(the_carrier(X0)) ),
inference(definition_unfolding,[],[f124,f142]) ).
tcf(c_49,negated_conjecture,
apply_as_element(the_carrier(sK0),the_carrier(sK0),identity_on_carrier(sK0),sK1) != sK1,
inference(cnf_transformation,[],[f119]) ).
tcf(c_50,negated_conjecture,
element(sK1,the_carrier(sK0)),
inference(cnf_transformation,[],[f118]) ).
tcf(c_51,negated_conjecture,
~ empty_carrier(sK0),
inference(cnf_transformation,[],[f117]) ).
tcf(c_52,negated_conjecture,
one_sorted_str(sK0),
inference(cnf_transformation,[],[f116]) ).
tcf(c_54,plain,
! [X0: $i] :
( function(identity_on_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_55,plain,
! [X0: $i] :
( quasi_total(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_56,plain,
! [X0: $i] :
( relation_of2_as_subset(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( identity_relation(the_carrier(X0)) = identity_on_carrier(X0) )
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_60,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| ( apply_as_element(X1,X2,X0,X3) = apply(X0,X3) )
| ~ function(X0)
| ~ element(X3,X1)
| ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_168,plain,
( empty_carrier(sK0)
| ~ one_sorted_str(sK0)
| ~ empty(the_carrier(sK0)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation_of2(X3,X1,X2)
| ~ one_sorted_str(X0)
| ( identity_on_carrier(X0) != X3 )
| ( the_carrier(X0) != X2 )
| ( the_carrier(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_73]) ).
tcf(c_730,plain,
! [X0: $i] :
( relation_of2(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(unflattening,[status(thm)],[c_729]) ).
tcf(c_754,plain,
! [X0: $i] :
( ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_60]) ).
tcf(c_755,plain,
( ~ one_sorted_str(sK0)
| ~ empty(the_carrier(sK0)) ),
inference(unflattening,[status(thm)],[c_754]) ).
tcf(c_756,plain,
~ empty(the_carrier(sK0)),
inference(global_subsumption_just,[status(thm)],[c_755,c_52,c_51,c_168]) ).
tcf(c_802,plain,
! [X0: $i] :
( relation_of2(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_730]) ).
tcf(c_803,plain,
relation_of2(identity_on_carrier(sK0),the_carrier(sK0),the_carrier(sK0)),
inference(unflattening,[status(thm)],[c_802]) ).
tcf(c_807,plain,
! [X0: $i] :
( ( identity_relation(the_carrier(X0)) = identity_on_carrier(X0) )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_57]) ).
tcf(c_808,plain,
identity_relation(the_carrier(sK0)) = identity_on_carrier(sK0),
inference(unflattening,[status(thm)],[c_807]) ).
tcf(c_812,plain,
! [X0: $i] :
( quasi_total(identity_on_carrier(X0),the_carrier(X0),the_carrier(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_55]) ).
tcf(c_813,plain,
quasi_total(identity_on_carrier(sK0),the_carrier(sK0),the_carrier(sK0)),
inference(unflattening,[status(thm)],[c_812]) ).
tcf(c_817,plain,
! [X0: $i] :
( function(identity_on_carrier(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_54]) ).
tcf(c_818,plain,
function(identity_on_carrier(sK0)),
inference(unflattening,[status(thm)],[c_817]) ).
tcf(c_4576,plain,
( empty(the_carrier(sK0))
| in(sK1,the_carrier(sK0)) ),
inference(superposition,[status(thm)],[c_50,c_98]) ).
tcf(c_4584,plain,
in(sK1,the_carrier(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_4576,c_756]) ).
tcf(c_4616,plain,
apply(identity_relation(the_carrier(sK0)),sK1) = sK1,
inference(superposition,[status(thm)],[c_4584,c_85]) ).
tcf(c_4620,plain,
apply(identity_on_carrier(sK0),sK1) = sK1,
inference(light_normalisation,[status(thm)],[c_4616,c_808]) ).
tcf(c_4753,plain,
! [X0: $i] :
( empty(the_carrier(sK0))
| ( apply_as_element(the_carrier(sK0),the_carrier(sK0),identity_on_carrier(sK0),X0) = apply(identity_on_carrier(sK0),X0) )
| ~ function(identity_on_carrier(sK0))
| ~ element(X0,the_carrier(sK0))
| ~ relation_of2(identity_on_carrier(sK0),the_carrier(sK0),the_carrier(sK0)) ),
inference(superposition,[status(thm)],[c_813,c_61]) ).
tcf(c_4767,plain,
! [X0: $i] :
( ( apply_as_element(the_carrier(sK0),the_carrier(sK0),identity_on_carrier(sK0),X0) = apply(identity_on_carrier(sK0),X0) )
| ~ element(X0,the_carrier(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4753,c_756,c_818,c_803]) ).
tcf(c_4788,plain,
apply_as_element(the_carrier(sK0),the_carrier(sK0),identity_on_carrier(sK0),sK1) = apply(identity_on_carrier(sK0),sK1),
inference(superposition,[status(thm)],[c_50,c_4767]) ).
tcf(c_4792,plain,
apply_as_element(the_carrier(sK0),the_carrier(sK0),identity_on_carrier(sK0),sK1) = sK1,
inference(light_normalisation,[status(thm)],[c_4788,c_4620]) ).
tcf(c_4793,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4792,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU353+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n018.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 13:50:53 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.42 % Detected problem language: tptp
% 0.14/5.43 % Proving...
% 3.62/6.28 % SZS status Started for theBenchmark.p
% 3.62/6.28 % SZS status Theorem for theBenchmark.p
% 3.62/6.28
% 3.62/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.62/6.28
% 3.62/6.28 % ------ iProver source info
% 3.62/6.28
% 3.62/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.62/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.62/6.28 % git: non_committed_changes: false
% 3.62/6.28
% 3.62/6.28 % ------ Parsing...
% 3.62/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.62/6.28
% 3.62/6.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 31 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 12 0s sf_e pe_s pe_e %
% 3.62/6.28
% 3.62/6.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.62/6.28
% 3.62/6.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.62/6.28 % ------ Proving...
% 3.62/6.28 % ------ Problem Properties
% 3.62/6.28
% 3.62/6.28 %
% 3.62/6.28 % clauses 56
% 3.62/6.28 % conjectures 2
% 3.62/6.28 % EPR 10
% 3.62/6.28 % Horn 51
% 3.62/6.28 % unary 42
% 3.62/6.28 % binary 7
% 3.62/6.28 % lits 86
% 3.62/6.28 % lits eq 7
% 3.62/6.28 % fd_pure 0
% 3.62/6.28 % fd_pseudo 0
% 3.62/6.28 % fd_cond 0
% 3.62/6.28 % fd_pseudo_cond 1
% 3.62/6.28 % AC symbols 0
% 3.62/6.28
% 3.62/6.28 % ------ Schedule dynamic 5 is on
% 3.62/6.28
% 3.62/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.62/6.28
% 3.62/6.28
% 3.62/6.28 % ------
% 3.62/6.28 % Current options:
% 3.62/6.28 % ------
% 3.62/6.28
% 3.62/6.28
% 3.62/6.28 %
% 3.62/6.28
% 3.62/6.28 % ------ Proving...
% 3.62/6.28 %
% 3.62/6.28
% 3.62/6.28 % SZS status Theorem for theBenchmark.p
% 3.62/6.28
% 3.62/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.62/6.29
% 3.62/6.29
%------------------------------------------------------------------------------