%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC339+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 03:09:22 PM UTC 2026
% Result : Theorem 3.19s 1.19s
% Output : CNFRefutation 3.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 14 unt; 0 def)
% Number of atoms : 212 ( 49 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 278 ( 101 ~; 92 |; 67 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 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 : 91 ( 0 sgn 63 !; 28 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( totalorderedP(X0)
& segmentP(X1,X0) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( totalorderedP(X0)
& segmentP(X1,X0) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f172,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f173,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(f174,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,[],[f173]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ totalorderedP(X0)
| ~ segmentP(X1,X0) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X12,X10)
| app(X13,cons(X12,nil)) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(cons(X10,nil),X11) != X5
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X6,X8)
| app(cons(X8,nil),X9) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != X4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3 ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ totalorderedP(X0)
| ~ segmentP(X1,X0) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X12,X10)
| app(X13,cons(X12,nil)) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(cons(X10,nil),X11) != X5
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X6,X8)
| app(cons(X8,nil),X9) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != X4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3 ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ~ totalorderedP(sK53)
| ~ segmentP(sK54,sK53) )
& ( nil != sK55
| nil = sK56 )
& ssList(sK57)
& ssList(sK58)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X12,X10)
| app(X13,cons(X12,nil)) != sK55
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(cons(X10,nil),X11) != sK58
| ~ ssList(X11) )
| ~ ssItem(X10) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X6,X8)
| app(cons(X8,nil),X9) != sK55
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != sK57
| ~ ssList(X7) )
| ~ ssItem(X6) )
& totalorderedP(sK55)
& sK56 = app(app(sK57,sK55),sK58)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58)],[f222]) ).
fof(f440,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f441,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,[],[f174]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ totalorderedP(sK53)
| ~ segmentP(sK54,sK53) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
ssList(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
ssList(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
totalorderedP(sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK56 = app(app(sK57,sK55),sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
( ~ totalorderedP(sK55)
| ~ segmentP(sK56,sK55) ),
inference(definition_unfolding,[],[f500,f509,f508,f508]) ).
fof(f512,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f508]) ).
tcf(c_192,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f440]) ).
tcf(c_193,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,[],[f441]) ).
tcf(c_246,negated_conjecture,
app(app(sK57,sK55),sK58) = sK56,
inference(cnf_transformation,[],[f507]) ).
tcf(c_247,negated_conjecture,
totalorderedP(sK55),
inference(cnf_transformation,[],[f506]) ).
tcf(c_250,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f503]) ).
tcf(c_251,negated_conjecture,
ssList(sK57),
inference(cnf_transformation,[],[f502]) ).
tcf(c_253,negated_conjecture,
( ~ totalorderedP(sK55)
| ~ segmentP(sK56,sK55) ),
inference(cnf_transformation,[],[f510]) ).
tcf(c_257,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f512]) ).
tcf(c_559,plain,
! [X0: $i] :
( segmentP(sK56,X0)
| ~ ssList(sK58)
| ~ ssList(sK55)
| ~ ssList(sK57)
| ~ ssList(X0)
| ~ segmentP(sK55,X0) ),
inference(superposition,[status(thm)],[c_246,c_193]) ).
tcf(c_1344,plain,
! [X0: $i] :
( segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_559,c_257,c_251,c_250,c_559]) ).
tcf(c_1345,plain,
! [X0: $i] :
( segmentP(sK56,X0)
| ~ ssList(X0)
| ~ segmentP(sK55,X0) ),
inference(renaming,[status(thm)],[c_1344]) ).
tcf(c_1353,plain,
( segmentP(sK56,sK55)
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_192,c_1345]) ).
tcf(c_1355,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1353,c_253,c_247,c_257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC339+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 17:44:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 3.19/1.19 % SZS status Started for theBenchmark.p
% 3.19/1.19 % SZS status Theorem for theBenchmark.p
% 3.19/1.19
% 3.19/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.19/1.19
% 3.19/1.19 % ------ iProver source info
% 3.19/1.19
% 3.19/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.19/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.19/1.19 % git: non_committed_changes: false
% 3.19/1.19
% 3.19/1.19 % ------ Parsing...
% 3.19/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.19/1.19 % ------ Proving...
% 3.19/1.19 % ------ Problem Properties
% 3.19/1.19
% 3.19/1.19 %
% 3.19/1.19 % clauses 209
% 3.19/1.19 % conjectures 12
% 3.19/1.19 % EPR 73
% 3.19/1.19 % Horn 138
% 3.19/1.19 % unary 20
% 3.19/1.19 % binary 55
% 3.19/1.19 % lits 696
% 3.19/1.19 % lits eq 88
% 3.19/1.19 % fd_pure 0
% 3.19/1.19 % fd_pseudo 0
% 3.19/1.19 % fd_cond 21
% 3.19/1.19 % fd_pseudo_cond 17
% 3.19/1.19 % AC symbols 0
% 3.19/1.19
% 3.19/1.19 % ------ Input Options Time Limit: Unbounded
% 3.19/1.19
% 3.19/1.19
% 3.19/1.19 % ------
% 3.19/1.19 % Current options:
% 3.19/1.19 % ------
% 3.19/1.19
% 3.19/1.19
% 3.19/1.19 %
% 3.19/1.19
% 3.19/1.19 % ------ Proving...
% 3.19/1.19 %
% 3.19/1.19
% 3.19/1.19 % SZS status Theorem for theBenchmark.p
% 3.19/1.19
% 3.19/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.19/1.19
% 3.19/1.19
%------------------------------------------------------------------------------