%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KRS251+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.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 01:54:27 PM UTC 2026
% Result : Theorem 6.39s 1.75s
% Output : CNFRefutation 6.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 7 unt; 0 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 162 ( 63 ~; 73 |; 16 &)
% ( 5 <=>; 2 =>; 0 <=; 3 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 101 !; 9 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ! [X2] :
( model(X2,X0)
=> model(X2,X1) )
<=> status(X0,X1,thm) ),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax',thm) ).
fof(f17,axiom,
! [X0,X1] :
( ? [X2] :
( model(X2,not(X1))
& model(X2,X0) )
<=> status(X0,X1,csa) ),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax',csa) ).
fof(f24,axiom,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
<~> status(X2,X3,X1) )
<=> xora(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax',xora) ).
fof(f25,axiom,
! [X0,X1] :
( model(X0,X1)
<~> model(X0,not(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax',completeness) ).
fof(f33,conjecture,
xora(csa,thm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xora_csa_thm) ).
fof(f34,negated_conjecture,
~ xora(csa,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
~ xora(csa,thm),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ! [X2,X3] :
( status(X2,X3,X0)
<~> status(X2,X3,X1) )
=> xora(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f37,plain,
! [X0,X1] :
( ! [X2] :
( ~ model(X2,X0)
| model(X2,X1) )
<=> status(X0,X1,thm) ),
inference(ennf_transformation,[],[f5]) ).
fof(f38,plain,
! [X0,X1] :
( ? [X2,X3] :
( status(X2,X3,X0)
<=> status(X2,X3,X1) )
| xora(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f40,plain,
! [X0,X1] :
( ( ? [X2] :
( model(X2,X0)
& ~ model(X2,X1) )
| status(X0,X1,thm) )
& ( ~ status(X0,X1,thm)
| ! [X2] :
( ~ model(X2,X0)
| model(X2,X1) ) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f41,plain,
! [X0,X1] :
( ( ? [X3] :
( model(X3,X0)
& ~ model(X3,X1) )
| status(X0,X1,thm) )
& ( ~ status(X0,X1,thm)
| ! [X2] :
( ~ model(X2,X0)
| model(X2,X1) ) ) ),
inference(rectify,[],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( ( model(sK0(X0,X1),X0)
& ~ model(sK0(X0,X1),X1) )
| status(X0,X1,thm) )
& ( ~ status(X0,X1,thm)
| ! [X2] :
( ~ model(X2,X0)
| model(X2,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ~ status(X2,X3,X0)
| status(X2,X3,X1) )
& ( ~ status(X2,X3,X1)
| status(X2,X3,X0) ) )
| xora(X0,X1) ),
inference(nnf_transformation,[],[f38]) ).
fof(f44,plain,
! [X0,X1] :
( ( ( ~ status(sK1(X0,X1),sK2(X0,X1),X0)
| status(sK1(X0,X1),sK2(X0,X1),X1) )
& ( ~ status(sK1(X0,X1),sK2(X0,X1),X1)
| status(sK1(X0,X1),sK2(X0,X1),X0) ) )
| xora(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X2,sK1(X0,X1)),skolemize(X3,sK2(X0,X1))],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ model(X2,not(X1))
| ~ model(X2,X0) )
| status(X0,X1,csa) )
& ( ~ status(X0,X1,csa)
| ? [X2] :
( model(X2,not(X1))
& model(X2,X0) ) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f46,plain,
! [X0,X1] :
( ( ! [X3] :
( ~ model(X3,not(X1))
| ~ model(X3,X0) )
| status(X0,X1,csa) )
& ( ~ status(X0,X1,csa)
| ? [X2] :
( model(X2,not(X1))
& model(X2,X0) ) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ( ! [X3] :
( ~ model(X3,not(X1))
| ~ model(X3,X0) )
| status(X0,X1,csa) )
& ( ~ status(X0,X1,csa)
| ( model(sK3(X0,X1),not(X1))
& model(sK3(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f46]) ).
fof(f55,plain,
! [X0,X1] :
( ( model(X0,X1)
| model(X0,not(X1)) )
& ( ~ model(X0,X1)
| ~ model(X0,not(X1)) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f56,plain,
~ xora(csa,thm),
inference(cnf_transformation,[],[f35]) ).
fof(f57,plain,
! [X0,X1] :
( model(sK0(X0,X1),X0)
| status(X0,X1,thm) ),
inference(cnf_transformation,[],[f42]) ).
fof(f58,plain,
! [X0,X1] :
( ~ model(sK0(X0,X1),X1)
| status(X0,X1,thm) ),
inference(cnf_transformation,[],[f42]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ status(X0,X1,thm)
| ~ model(X2,X0)
| model(X2,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f60,plain,
! [X0,X1] :
( ~ status(sK1(X0,X1),sK2(X0,X1),X0)
| status(sK1(X0,X1),sK2(X0,X1),X1)
| xora(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f61,plain,
! [X0,X1] :
( ~ status(sK1(X0,X1),sK2(X0,X1),X1)
| status(sK1(X0,X1),sK2(X0,X1),X0)
| xora(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f62,plain,
! [X3,X0,X1] :
( ~ model(X3,not(X1))
| ~ model(X3,X0)
| status(X0,X1,csa) ),
inference(cnf_transformation,[],[f47]) ).
fof(f63,plain,
! [X0,X1] :
( ~ status(X0,X1,csa)
| model(sK3(X0,X1),not(X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f64,plain,
! [X0,X1] :
( ~ status(X0,X1,csa)
| model(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f82,plain,
! [X0,X1] :
( model(X0,X1)
| model(X0,not(X1)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f83,plain,
! [X0,X1] :
( ~ model(X0,X1)
| ~ model(X0,not(X1)) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_49,negated_conjecture,
~ xora(csa,thm),
inference(cnf_transformation,[],[f56]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( model(X2,X1)
| ~ model(X2,X0)
| ~ status(X0,X1,thm) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( status(X0,X1,thm)
| ~ model(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( status(X0,X1,thm)
| model(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( xora(X0,X1)
| status(sK1(X0,X1),sK2(X0,X1),X0)
| ~ status(sK1(X0,X1),sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( xora(X0,X1)
| status(sK1(X0,X1),sK2(X0,X1),X1)
| ~ status(sK1(X0,X1),sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( model(sK3(X0,X1),X0)
| ~ status(X0,X1,csa) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( model(sK3(X0,X1),not(X1))
| ~ status(X0,X1,csa) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( status(X2,X1,csa)
| ~ model(X0,X2)
| ~ model(X0,not(X1)) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ~ model(X0,X1)
| ~ model(X0,not(X1)) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( model(X0,X1)
| model(X0,not(X1)) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( model(X0,not(X1))
| model(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_76]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( model(X0,X1)
| model(X0,not(X1)) ),
inference(renaming,[status(thm)],[c_88]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] :
( model(X0,X2)
| status(X1,X2,csa)
| ~ model(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_57,c_89]) ).
tcf(c_239,plain,
( status(sK1(csa,thm),sK2(csa,thm),thm)
| ~ status(sK1(csa,thm),sK2(csa,thm),csa) ),
inference(resolution,[status(thm)],[c_49,c_54]) ).
tcf(c_246,plain,
( status(sK1(csa,thm),sK2(csa,thm),csa)
| ~ status(sK1(csa,thm),sK2(csa,thm),thm) ),
inference(resolution,[status(thm)],[c_49,c_53]) ).
tcf(c_263,plain,
( status(sK1(csa,thm),sK2(csa,thm),thm)
| ~ status(sK1(csa,thm),sK2(csa,thm),csa) ),
inference(prop_impl_just,[status(thm)],[c_239]) ).
tcf(c_457,plain,
( model(sK3(sK1(csa,thm),sK2(csa,thm)),not(sK2(csa,thm)))
| ~ status(sK1(csa,thm),sK2(csa,thm),csa) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_458,plain,
( model(sK3(sK1(csa,thm),sK2(csa,thm)),sK1(csa,thm))
| ~ status(sK1(csa,thm),sK2(csa,thm),csa) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_868,plain,
! [X0: $i,X1: $i,X2: $i] :
( status(X0,X2,csa)
| status(X0,X1,thm)
| model(sK0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_52,c_154]) ).
tcf(c_2505,plain,
! [X0: $i,X1: $i] :
( status(X0,X1,thm)
| status(X0,X1,csa) ),
inference(superposition,[status(thm)],[c_868,c_51]) ).
tcf(c_2731,plain,
status(sK1(csa,thm),sK2(csa,thm),thm),
inference(backward_subsumption_resolution,[status(thm)],[c_263,c_2505]) ).
tcf(c_2913,plain,
! [X0: $i] :
( model(sK3(sK1(csa,thm),sK2(csa,thm)),X0)
| ~ status(sK1(csa,thm),X0,thm)
| ~ model(sK3(sK1(csa,thm),sK2(csa,thm)),sK1(csa,thm)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_3029,plain,
( ~ model(sK3(sK1(csa,thm),sK2(csa,thm)),sK2(csa,thm))
| ~ model(sK3(sK1(csa,thm),sK2(csa,thm)),not(sK2(csa,thm))) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_17664,plain,
( model(sK3(sK1(csa,thm),sK2(csa,thm)),sK2(csa,thm))
| ~ status(sK1(csa,thm),sK2(csa,thm),thm)
| ~ model(sK3(sK1(csa,thm),sK2(csa,thm)),sK1(csa,thm)) ),
inference(instantiation,[status(thm)],[c_2913]) ).
tcf(c_17665,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_17664,c_3029,c_2731,c_457,c_458,c_246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS251+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n013.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 19:48:51 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 6.39/1.75 % SZS status Started for theBenchmark.p
% 6.39/1.75 % SZS status Theorem for theBenchmark.p
% 6.39/1.75
% 6.39/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.39/1.75
% 6.39/1.75 % ------ iProver source info
% 6.39/1.75
% 6.39/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 6.39/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.39/1.75 % git: non_committed_changes: false
% 6.39/1.75
% 6.39/1.75 % ------ Parsing...
% 6.39/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.39/1.75
% 6.39/1.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 6.39/1.75
% 6.39/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 6.39/1.75 % ------ Proving...
% 6.39/1.75 % ------ Problem Properties
% 6.39/1.75
% 6.39/1.75 %
% 6.39/1.75 % clauses 25
% 6.39/1.75 % conjectures 0
% 6.39/1.75 % EPR 17
% 6.39/1.75 % Horn 22
% 6.39/1.75 % unary 13
% 6.39/1.75 % binary 10
% 6.39/1.75 % lits 39
% 6.39/1.75 % lits eq 0
% 6.39/1.75 % fd_pure 0
% 6.39/1.75 % fd_pseudo 0
% 6.39/1.75 % fd_cond 0
% 6.39/1.75 % fd_pseudo_cond 0
% 6.39/1.75 % AC symbols 0
% 6.39/1.75
% 6.39/1.75 % ------ Schedule dynamic 5 is on
% 6.39/1.75
% 6.39/1.75 % ------ no conjectures: strip conj schedule
% 6.39/1.75
% 6.39/1.75 % ------ no equalities: superposition off
% 6.39/1.75
% 6.39/1.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 6.39/1.75
% 6.39/1.75
% 6.39/1.75 % ------
% 6.39/1.75 % Current options:
% 6.39/1.75 % ------
% 6.39/1.75
% 6.39/1.75
% 6.39/1.75 %
% 6.39/1.75
% 6.39/1.75 % ------ Proving...
% 6.39/1.75 %
% 6.39/1.75
% 6.39/1.75 % SZS status Theorem for theBenchmark.p
% 6.39/1.75
% 6.39/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.39/1.75
% 6.39/1.75
%------------------------------------------------------------------------------