%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC076+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 : 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 03:07:47 PM UTC 2026
% Result : Theorem 3.99s 7.23s
% Output : CNFRefutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 63 ( 17 unt; 0 def)
% Number of atoms : 308 ( 99 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 409 ( 164 ~; 150 |; 70 &)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 87 !; 26 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
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(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( app(X12,cons(X10,nil)) = X2
& ssList(X12) )
& app(cons(X10,nil),X11) = X6
& ssList(X11) )
& ssItem(X10) )
| ? [X7] :
( ? [X8] :
( ? [X9] :
( app(cons(X7,nil),X9) = X2
& ssList(X9) )
& app(X8,cons(X7,nil)) = X5
& ssList(X8) )
& ssItem(X7) )
| ~ equalelemsP(X2)
| app(app(X5,X2),X6) != X3 ) ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| 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)
=> ( ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( app(X12,cons(X10,nil)) = X2
& ssList(X12) )
& app(cons(X10,nil),X11) = X6
& ssList(X11) )
& ssItem(X10) )
| ? [X7] :
( ? [X8] :
( ? [X9] :
( app(cons(X7,nil),X9) = X2
& ssList(X9) )
& app(X8,cons(X7,nil)) = X5
& ssList(X8) )
& ssItem(X7) )
| ~ equalelemsP(X2)
| app(app(X5,X2),X6) != X3 ) ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| 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)
& ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( app(X12,cons(X10,nil)) != X2
| ~ ssList(X12) )
| app(cons(X10,nil),X11) != X6
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(cons(X7,nil),X9) != X2
| ~ ssList(X9) )
| app(X8,cons(X7,nil)) != X5
| ~ ssList(X8) )
| ~ ssItem(X7) )
& equalelemsP(X2)
& app(app(X5,X2),X6) = X3 ) )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( app(X12,cons(X10,nil)) != X2
| ~ ssList(X12) )
| app(cons(X10,nil),X11) != X6
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(cons(X7,nil),X9) != X2
| ~ ssList(X9) )
| app(X8,cons(X7,nil)) != X5
| ~ ssList(X8) )
| ~ ssItem(X7) )
& equalelemsP(X2)
& app(app(X5,X2),X6) = X3 ) )
& ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,plain,
! [X0] :
( ~ ssList(X0)
| ( segmentP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f122,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X2,X0),X3),X1) ) ) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f123,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X2,X0),X3),X1) ) ) ) ),
inference(flattening,[],[f122]) ).
fof(f124,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f133,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( nil != sK0
| nil != sK1 )
& ( nil != sK2
| nil = sK3 )
& ssList(sK4)
& ssList(sK5)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( app(X12,cons(X10,nil)) != sK2
| ~ ssList(X12) )
| app(cons(X10,nil),X11) != sK5
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( app(cons(X7,nil),X9) != sK2
| ~ ssList(X9) )
| app(X8,cons(X7,nil)) != sK4
| ~ ssList(X8) )
| ~ ssItem(X7) )
& equalelemsP(sK2)
& sK3 = app(app(sK4,sK2),sK5)
& ! [X4] :
( ~ segmentP(sK0,X4)
| ~ segmentP(sK1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X5,sK4),skolemize(X6,sK5)],[f99]) ).
fof(f138,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f140,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ segmentP(nil,X0)
| nil = X0 )
& ( nil != X0
| segmentP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f120]) ).
fof(f147,plain,
ssList(sK0),
inference(cnf_transformation,[],[f133]) ).
fof(f151,plain,
( nil != sK0
| nil != sK1 ),
inference(cnf_transformation,[],[f133]) ).
fof(f152,plain,
( nil != sK2
| nil = sK3 ),
inference(cnf_transformation,[],[f133]) ).
fof(f153,plain,
ssList(sK4),
inference(cnf_transformation,[],[f133]) ).
fof(f154,plain,
ssList(sK5),
inference(cnf_transformation,[],[f133]) ).
fof(f158,plain,
sK3 = app(app(sK4,sK2),sK5),
inference(cnf_transformation,[],[f133]) ).
fof(f159,plain,
! [X4] :
( ~ segmentP(sK0,X4)
| ~ segmentP(sK1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f133]) ).
fof(f160,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f133]) ).
fof(f161,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f133]) ).
fof(f185,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f188,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f189,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f140]) ).
fof(f192,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X2,X0),X3),X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f193,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f209,plain,
! [X4] :
( ~ segmentP(sK2,X4)
| ~ segmentP(sK3,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f159,f161,f160]) ).
fof(f210,plain,
( nil != sK2
| nil != sK3 ),
inference(definition_unfolding,[],[f151,f161,f160]) ).
fof(f212,plain,
ssList(sK2),
inference(definition_unfolding,[],[f147,f160]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_50,negated_conjecture,
app(app(sK4,sK2),sK5) = sK3,
inference(cnf_transformation,[],[f158]) ).
tcf(c_54,negated_conjecture,
ssList(sK5),
inference(cnf_transformation,[],[f154]) ).
tcf(c_55,negated_conjecture,
ssList(sK4),
inference(cnf_transformation,[],[f153]) ).
tcf(c_56,negated_conjecture,
( ( nil = sK3 )
| ( nil != sK2 ) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_57,negated_conjecture,
( ( nil != sK2 )
| ( nil != sK3 ) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_61,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f212]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_88,plain,
ssList(nil),
inference(cnf_transformation,[],[f188]) ).
tcf(c_90,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_93,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_109,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_118,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_139,negated_conjecture,
nil != sK2,
inference(global_subsumption_just,[status(thm)],[c_56,c_56,c_57]) ).
tcf(c_842,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0)
| ( X2 != nil )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_84]) ).
tcf(c_843,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0) ),
inference(unflattening,[status(thm)],[c_842]) ).
tcf(c_845,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_843,c_88,c_843]) ).
tcf(c_846,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sK2,X0)
| ~ segmentP(sK3,X0) ),
inference(renaming,[status(thm)],[c_845]) ).
tcf(c_2051,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3345,plain,
! [X0: $i] :
( ( nil = sK2 )
| ( sK2 != X0 )
| ( nil != X0 ) ),
inference(instantiation,[status(thm)],[c_2051]) ).
tcf(c_3346,plain,
( ( nil = sK2 )
| ( sK2 != nil )
| ( nil != nil ) ),
inference(instantiation,[status(thm)],[c_3345]) ).
tcf(c_3555,plain,
( ( sK2 = nil )
| ~ ssList(sK2)
| ~ segmentP(sK2,sK2)
| ~ segmentP(sK3,sK2) ),
inference(instantiation,[status(thm)],[c_846]) ).
tcf(c_4877,plain,
! [X0: $i] :
( segmentP(sK3,X0)
| ~ ssList(sK5)
| ~ ssList(sK4)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ segmentP(sK2,X0) ),
inference(superposition,[status(thm)],[c_50,c_92]) ).
tcf(c_4910,plain,
! [X0: $i] :
( segmentP(sK3,X0)
| ~ ssList(X0)
| ~ segmentP(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4877,c_54,c_55,c_61]) ).
tcf(c_5278,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_93,c_4910]) ).
tcf(c_5279,plain,
segmentP(sK3,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_5278,c_61]) ).
tcf(c_6169,plain,
( segmentP(sK2,sK2)
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_6170,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6169,c_5279,c_3555,c_3346,c_139,c_118,c_109,c_88,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC076+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/6.42 % Computer : n013.cluster.edu
% 0.12/6.42 % Model : x86_64 x86_64
% 0.12/6.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/6.42 % Memory : 8046.5625MB
% 0.12/6.42 % OS : Linux 6.8.0-71-generic
% 0.12/6.42 % CPULimit : 300
% 0.12/6.42 % WCLimit : 300
% 0.12/6.42 % DateTime : Thu Sep 24 16:15:06 UTC 2026
% 0.12/6.42 % CPUTime :
% 0.12/6.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/6.46 Running first-order theorem proving
% 0.15/6.46 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
% 0.15/6.47
% 0.15/6.47 % ======== iProver multi-core TPTP/SMT =========
% 0.15/6.47
% 0.15/6.48 % Detected problem language: tptp
% 0.15/6.49 % Proving...
% 3.99/7.23 % SZS status Started for theBenchmark.p
% 3.99/7.23 % SZS status Theorem for theBenchmark.p
% 3.99/7.23
% 3.99/7.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.99/7.23
% 3.99/7.23 % ------ iProver source info
% 3.99/7.23
% 3.99/7.23 % git: date: 2026-07-19 20:42:38 +0200
% 3.99/7.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.99/7.23 % git: non_committed_changes: false
% 3.99/7.23
% 3.99/7.23 % ------ Parsing...
% 3.99/7.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.99/7.23
% 3.99/7.23 % ------ 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 %
% 3.99/7.23
% 3.99/7.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.99/7.23
% 3.99/7.23 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.99/7.23 % ------ Proving...
% 3.99/7.23 % ------ Problem Properties
% 3.99/7.23
% 3.99/7.23 %
% 3.99/7.23 % clauses 53
% 3.99/7.23 % conjectures 9
% 3.99/7.23 % EPR 18
% 3.99/7.23 % Horn 45
% 3.99/7.23 % unary 14
% 3.99/7.23 % binary 5
% 3.99/7.23 % lits 162
% 3.99/7.23 % lits eq 38
% 3.99/7.23 % fd_pure 0
% 3.99/7.23 % fd_pseudo 0
% 3.99/7.23 % fd_cond 6
% 3.99/7.23 % fd_pseudo_cond 6
% 3.99/7.23 % AC symbols 0
% 3.99/7.23
% 3.99/7.23 % ------ Schedule dynamic 5 is on
% 3.99/7.23
% 3.99/7.23 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.99/7.23
% 3.99/7.23
% 3.99/7.23 % ------
% 3.99/7.23 % Current options:
% 3.99/7.23 % ------
% 3.99/7.23
% 3.99/7.23
% 3.99/7.23 %
% 3.99/7.23
% 3.99/7.23 % ------ Proving...
% 3.99/7.23 %
% 3.99/7.23
% 3.99/7.23 % SZS status Theorem for theBenchmark.p
% 3.99/7.23
% 3.99/7.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.99/7.23
% 3.99/7.23
%------------------------------------------------------------------------------