%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC404+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 : n026.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 03:09:39 PM UTC 2026
% Result : Theorem 4.48s 6.31s
% Output : CNFRefutation 4.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 49 ( 20 unt; 0 def)
% Number of atoms : 279 ( 49 equ)
% Maximal formula atoms : 29 ( 5 avg)
% Number of connectives : 371 ( 141 ~; 134 |; 75 &)
% ( 2 <=>; 19 =>; 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 81 !; 30 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X14] :
( ssItem(X14)
=> ( memberP(X1,X14)
| ~ memberP(X0,X14) ) )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( lt(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] :
( lt(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ strictorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| 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 = X2
& nil != X3 )
| ! [X14] :
( ssItem(X14)
=> ( memberP(X1,X14)
| ~ memberP(X0,X14) ) )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( lt(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] :
( lt(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ strictorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f146,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X2
| nil = X3 )
& ? [X14] :
( ssItem(X14)
& ~ memberP(X1,X14)
& memberP(X0,X14) )
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ lt(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] :
( ~ lt(X6,X8)
| app(cons(X8,nil),X9) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != X4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& strictorderedP(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)
& ( nil != X2
| nil = X3 )
& ? [X14] :
( ssItem(X14)
& ~ memberP(X1,X14)
& memberP(X0,X14) )
& ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ lt(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] :
( ~ lt(X6,X8)
| app(cons(X8,nil),X9) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != X4
| ~ ssList(X7) )
| ~ ssItem(X6) )
& strictorderedP(X2)
& app(app(X4,X2),X5) = X3 ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f277,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f146]) ).
fof(f278,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(flattening,[],[f277]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( nil != sK55
| nil = sK56 )
& ssItem(sK59)
& ~ memberP(sK54,sK59)
& memberP(sK53,sK59)
& ssList(sK57)
& ssList(sK58)
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ lt(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] :
( ~ lt(X6,X8)
| app(cons(X8,nil),X9) != sK55
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(X7,cons(X6,nil)) != sK57
| ~ ssList(X7) )
| ~ ssItem(X6) )
& strictorderedP(sK55)
& sK56 = app(app(sK57,sK55),sK58)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58),skolemize(X14,sK59)],[f222]) ).
fof(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f414,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
ssItem(sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
~ memberP(sK54,sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
memberP(sK53,sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
ssList(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
ssList(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK56 = app(app(sK57,sK55),sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
memberP(sK55,sK59),
inference(definition_unfolding,[],[f503,f510]) ).
fof(f513,plain,
~ memberP(sK56,sK59),
inference(definition_unfolding,[],[f502,f511]) ).
fof(f515,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f510]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f415]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f414]) ).
tcf(c_246,negated_conjecture,
app(app(sK57,sK55),sK58) = sK56,
inference(cnf_transformation,[],[f509]) ).
tcf(c_250,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f505]) ).
tcf(c_251,negated_conjecture,
ssList(sK57),
inference(cnf_transformation,[],[f504]) ).
tcf(c_252,negated_conjecture,
memberP(sK55,sK59),
inference(cnf_transformation,[],[f512]) ).
tcf(c_253,negated_conjecture,
~ memberP(sK56,sK59),
inference(cnf_transformation,[],[f513]) ).
tcf(c_254,negated_conjecture,
ssItem(sK59),
inference(cnf_transformation,[],[f501]) ).
tcf(c_259,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f515]) ).
tcf(c_490,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ~ ssList(sK58)
| ~ ssItem(X0)
| ~ ssList(app(sK57,sK55))
| ~ memberP(app(sK57,sK55),X0) ),
inference(superposition,[status(thm)],[c_246,c_165]) ).
tcf(c_990,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ~ memberP(app(sK57,sK55),X0)
| ~ ssList(app(sK57,sK55))
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_490,c_250,c_490]) ).
tcf(c_991,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ~ ssItem(X0)
| ~ ssList(app(sK57,sK55))
| ~ memberP(app(sK57,sK55),X0) ),
inference(renaming,[status(thm)],[c_990]) ).
tcf(c_1002,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ~ ssList(sK55)
| ~ ssList(sK57)
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(app(sK57,sK55)) ),
inference(superposition,[status(thm)],[c_166,c_991]) ).
tcf(c_1084,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ~ ssList(sK58)
| ~ ssItem(X0)
| ~ ssList(app(sK57,sK55))
| ~ memberP(app(sK57,sK55),X0) ),
inference(superposition,[status(thm)],[c_246,c_165]) ).
tcf(c_1979,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ~ memberP(app(sK57,sK55),X0)
| ~ ssList(app(sK57,sK55))
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1084,c_991]) ).
tcf(c_1980,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ~ ssItem(X0)
| ~ ssList(app(sK57,sK55))
| ~ memberP(app(sK57,sK55),X0) ),
inference(renaming,[status(thm)],[c_1979]) ).
tcf(c_1990,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ~ ssList(sK55)
| ~ ssList(sK57)
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(app(sK57,sK55)) ),
inference(superposition,[status(thm)],[c_166,c_1980]) ).
tcf(c_2368,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ~ ssItem(X0)
| ~ memberP(sK55,X0)
| ~ ssList(app(sK57,sK55)) ),
inference(global_subsumption_just,[status(thm)],[c_1002,c_259,c_251,c_1002]) ).
tcf(c_2379,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ~ ssList(sK55)
| ~ ssList(sK57)
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(superposition,[status(thm)],[c_153,c_2368]) ).
tcf(c_3982,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ~ ssItem(X0)
| ~ memberP(sK55,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1990,c_259,c_251,c_2379]) ).
tcf(c_3991,plain,
( memberP(sK56,sK59)
| ~ ssItem(sK59) ),
inference(superposition,[status(thm)],[c_252,c_3982]) ).
tcf(c_3992,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3991,c_253,c_254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC404+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n026.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Thu Sep 24 18:07:15 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.42 Running first-order theorem proving
% 0.13/5.42 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
% 0.13/5.44
% 0.13/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.44
% 0.13/5.44 % Detected problem language: tptp
% 0.13/5.45 % Proving...
% 4.48/6.31 % SZS status Started for theBenchmark.p
% 4.48/6.31 % SZS status Theorem for theBenchmark.p
% 4.48/6.31
% 4.48/6.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.48/6.31
% 4.48/6.31 % ------ iProver source info
% 4.48/6.31
% 4.48/6.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.48/6.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.48/6.31 % git: non_committed_changes: false
% 4.48/6.31
% 4.48/6.31 % ------ Parsing...
% 4.48/6.31 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.48/6.31 % ------ Proving...
% 4.48/6.31 % ------ Problem Properties
% 4.48/6.31
% 4.48/6.31 %
% 4.48/6.31 % clauses 211
% 4.48/6.31 % conjectures 14
% 4.48/6.31 % EPR 75
% 4.48/6.31 % Horn 140
% 4.48/6.31 % unary 23
% 4.48/6.31 % binary 54
% 4.48/6.31 % lits 697
% 4.48/6.31 % lits eq 88
% 4.48/6.31 % fd_pure 0
% 4.48/6.31 % fd_pseudo 0
% 4.48/6.31 % fd_cond 21
% 4.48/6.31 % fd_pseudo_cond 17
% 4.48/6.31 % AC symbols 0
% 4.48/6.31
% 4.48/6.31 % ------ Input Options Time Limit: Unbounded
% 4.48/6.31
% 4.48/6.31
% 4.48/6.31 % ------
% 4.48/6.31 % Current options:
% 4.48/6.31 % ------
% 4.48/6.31
% 4.48/6.31
% 4.48/6.31 %
% 4.48/6.31
% 4.48/6.31 % ------ Proving...
% 4.48/6.31 %
% 4.48/6.31
% 4.48/6.31 % SZS status Theorem for theBenchmark.p
% 4.48/6.31
% 4.48/6.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.48/6.31
% 4.48/6.31
%------------------------------------------------------------------------------