%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC332+1 : TPTP v9.3.1. Released v2.4.0.
% 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 03:09:20 PM UTC 2026
% Result : Theorem 1.17s 1.21s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 66 ( 22 unt; 0 def)
% Number of atoms : 208 ( 52 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 227 ( 85 ~; 85 |; 38 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 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 : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 42 !; 12 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax73) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax74) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( equalelemsP(X0)
& segmentP(X1,X0) )
| ( neq(X3,nil)
& ~ singletonP(X2) )
| ~ segmentP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( equalelemsP(X0)
& segmentP(X1,X0) )
| ( neq(X3,nil)
& ~ singletonP(X2) )
| ~ segmentP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ equalelemsP(X0)
| ~ segmentP(X1,X0) )
& ( ~ neq(X3,nil)
| singletonP(X2) )
& segmentP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ equalelemsP(X0)
| ~ segmentP(X1,X0) )
& ( ~ neq(X3,nil)
| singletonP(X2) )
& segmentP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f105,plain,
! [X0] :
( ~ ssList(X0)
| ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f106,plain,
! [X0] :
( ~ ssList(X0)
| ( segmentP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f116,plain,
! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ),
inference(ennf_transformation,[],[f73]) ).
fof(f134,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ~ equalelemsP(sK0)
| ~ segmentP(sK1,sK0) )
& ( ~ neq(sK3,nil)
| singletonP(sK2) )
& segmentP(sK3,sK2)
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f136,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f139,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(nnf_transformation,[],[f105]) ).
fof(f140,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(rectify,[],[f139]) ).
fof(f141,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ( cons(sK8(X0),nil) = X0
& ssItem(sK8(X0)) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0))],[f140]) ).
fof(f142,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ segmentP(nil,X0)
| nil = X0 )
& ( nil != X0
| segmentP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f106]) ).
fof(f151,plain,
ssList(sK0),
inference(cnf_transformation,[],[f134]) ).
fof(f152,plain,
ssList(sK1),
inference(cnf_transformation,[],[f134]) ).
fof(f155,plain,
( ~ equalelemsP(sK0)
| ~ segmentP(sK1,sK0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f156,plain,
( ~ neq(sK3,nil)
| singletonP(sK2) ),
inference(cnf_transformation,[],[f134]) ).
fof(f157,plain,
segmentP(sK3,sK2),
inference(cnf_transformation,[],[f134]) ).
fof(f158,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f134]) ).
fof(f159,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f134]) ).
fof(f164,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f171,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f173,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| cons(sK8(X0),nil) = X0 ),
inference(cnf_transformation,[],[f141]) ).
fof(f174,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| ssItem(sK8(X0)) ),
inference(cnf_transformation,[],[f141]) ).
fof(f176,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f142]) ).
fof(f187,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f188,plain,
! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f211,plain,
( ~ equalelemsP(sK2)
| ~ segmentP(sK3,sK2) ),
inference(definition_unfolding,[],[f155,f159,f158,f158]) ).
fof(f212,plain,
ssList(sK3),
inference(definition_unfolding,[],[f152,f159]) ).
fof(f213,plain,
ssList(sK2),
inference(definition_unfolding,[],[f151,f158]) ).
tcf(c_49,negated_conjecture,
segmentP(sK3,sK2),
inference(cnf_transformation,[],[f157]) ).
tcf(c_50,negated_conjecture,
( singletonP(sK2)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_51,negated_conjecture,
( ~ equalelemsP(sK2)
| ~ segmentP(sK3,sK2) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_54,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f212]) ).
tcf(c_55,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f213]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_67,plain,
ssList(nil),
inference(cnf_transformation,[],[f171]) ).
tcf(c_70,plain,
! [X0: $i] :
( ssItem(sK8(X0))
| ~ ssList(X0)
| ~ singletonP(X0) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_71,plain,
! [X0: $i] :
( ( cons(sK8(X0),nil) = X0 )
| ~ ssList(X0)
| ~ singletonP(X0) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_73,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_83,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f187]) ).
tcf(c_84,plain,
! [X0: $i] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_136,negated_conjecture,
~ equalelemsP(sK2),
inference(global_subsumption_just,[status(thm)],[c_51,c_49,c_51]) ).
tcf(c_892,plain,
! [X0: $i,X1: $i] :
( singletonP(sK2)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_59]) ).
tcf(c_893,plain,
( singletonP(sK2)
| ( sK3 = nil )
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(unflattening,[status(thm)],[c_892]) ).
tcf(c_894,plain,
( singletonP(sK2)
| ( sK3 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_893,c_54,c_67,c_893]) ).
tcf(c_929,plain,
! [X0: $i] :
( ssItem(sK8(X0))
| ( sK3 = nil )
| ~ ssList(X0)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_894,c_70]) ).
tcf(c_930,plain,
( ssItem(sK8(sK2))
| ( sK3 = nil )
| ~ ssList(sK2) ),
inference(unflattening,[status(thm)],[c_929]) ).
tcf(c_931,plain,
( ssItem(sK8(sK2))
| ( sK3 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_930,c_55,c_930]) ).
tcf(c_3209,plain,
( ( sK3 = nil )
| ( cons(sK8(sK2),nil) = sK2 )
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_894,c_71]) ).
tcf(c_3211,plain,
( ( sK3 = nil )
| ( cons(sK8(sK2),nil) = sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3209,c_55]) ).
tcf(c_3224,plain,
( equalelemsP(sK2)
| ( sK3 = nil )
| ~ ssItem(sK8(sK2)) ),
inference(superposition,[status(thm)],[c_3211,c_84]) ).
tcf(c_3225,plain,
( ( sK3 = nil )
| ~ ssItem(sK8(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3224,c_136]) ).
tcf(c_3229,plain,
sK3 = nil,
inference(global_subsumption_just,[status(thm)],[c_3225,c_931,c_3225]) ).
tcf(c_3234,plain,
segmentP(nil,sK2),
inference(demodulation,[status(thm)],[c_49,c_3229]) ).
tcf(c_3236,plain,
( ( sK2 = nil )
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_3234,c_73]) ).
tcf(c_3237,plain,
sK2 = nil,
inference(forward_subsumption_resolution,[status(thm)],[c_3236,c_55]) ).
tcf(c_3241,plain,
~ equalelemsP(nil),
inference(demodulation,[status(thm)],[c_136,c_3237]) ).
tcf(c_3243,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3241,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC332+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 17:42:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 1.17/1.21 % SZS status Started for theBenchmark.p
% 1.17/1.21 % SZS status Theorem for theBenchmark.p
% 1.17/1.21
% 1.17/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.17/1.21
% 1.17/1.21 % ------ iProver source info
% 1.17/1.21
% 1.17/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 1.17/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.17/1.21 % git: non_committed_changes: false
% 1.17/1.21
% 1.17/1.21 % ------ Parsing...
% 1.17/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.17/1.21
% 1.17/1.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.17/1.21
% 1.17/1.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.17/1.21
% 1.17/1.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.17/1.21 % ------ Proving...
% 1.17/1.21 % ------ Problem Properties
% 1.17/1.21
% 1.17/1.21 %
% 1.17/1.21 % clauses 52
% 1.17/1.21 % conjectures 4
% 1.17/1.21 % EPR 17
% 1.17/1.21 % Horn 43
% 1.17/1.21 % unary 12
% 1.17/1.21 % binary 6
% 1.17/1.21 % lits 157
% 1.17/1.21 % lits eq 33
% 1.17/1.21 % fd_pure 0
% 1.17/1.21 % fd_pseudo 0
% 1.17/1.21 % fd_cond 5
% 1.17/1.21 % fd_pseudo_cond 6
% 1.17/1.21 % AC symbols 0
% 1.17/1.21
% 1.17/1.21 % ------ Schedule dynamic 5 is on
% 1.17/1.21
% 1.17/1.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.17/1.21
% 1.17/1.21
% 1.17/1.21 % ------
% 1.17/1.21 % Current options:
% 1.17/1.21 % ------
% 1.17/1.21
% 1.17/1.21
% 1.17/1.21 %
% 1.17/1.21
% 1.17/1.21 % ------ Proving...
% 1.17/1.21 %
% 1.17/1.21
% 1.17/1.21 % SZS status Theorem for theBenchmark.p
% 1.17/1.21
% 1.17/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.17/1.21
% 1.17/1.21
%------------------------------------------------------------------------------