%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC387+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 : n011.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 03:09:34 PM UTC 2026
% Result : Theorem 2.61s 6.07s
% Output : CNFRefutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 56 ( 15 unt; 1 def)
% Number of atoms : 211 ( 94 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 252 ( 100 ~; 94 |; 44 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 33 !; 12 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| cons(X5,nil) != X2 ) ) )
| ( nil = X0
& nil = X1 )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( memberP(X1,X4)
& cons(X4,nil) = X0
& ssItem(X4) )
| 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)
=> ( ( neq(X3,nil)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| cons(X5,nil) != X2 ) ) )
| ( nil = X0
& nil = X1 )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( memberP(X1,X4)
& cons(X4,nil) = X0
& ssItem(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ neq(X3,nil)
| ? [X5] :
( ssItem(X5)
& memberP(X3,X5)
& cons(X5,nil) = X2 ) )
& ( nil != X0
| nil != X1 )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ~ memberP(X1,X4)
| cons(X4,nil) != X0
| ~ ssItem(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ neq(X3,nil)
| ? [X5] :
( ssItem(X5)
& memberP(X3,X5)
& cons(X5,nil) = X2 ) )
& ( nil != X0
| nil != X1 )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ~ memberP(X1,X4)
| cons(X4,nil) != X0
| ~ ssItem(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ~ neq(sK56,nil)
| ( ssItem(sK57)
& memberP(sK56,sK57)
& sK55 = cons(sK57,nil) ) )
& ( nil != sK53
| nil != sK54 )
& ( nil != sK56
| nil = sK55 )
& ! [X4] :
( ~ memberP(sK54,X4)
| cons(X4,nil) != sK53
| ~ ssItem(X4) )
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X5,sK57)],[f222]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( ~ neq(sK56,nil)
| memberP(sK56,sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( ~ neq(sK56,nil)
| sK55 = cons(sK57,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( nil != sK53
| nil != sK54 ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
! [X4] :
( ~ memberP(sK54,X4)
| cons(X4,nil) != sK53
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
! [X4] :
( ~ memberP(sK56,X4)
| cons(X4,nil) != sK55
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f505,f506,f507]) ).
fof(f509,plain,
( nil != sK55
| nil != sK56 ),
inference(definition_unfolding,[],[f503,f507,f506]) ).
fof(f510,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f507]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_246,negated_conjecture,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(sK56,X0)
| ( cons(X0,nil) != sK55 ) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_247,negated_conjecture,
( ( nil = sK55 )
| ( nil != sK56 ) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_248,negated_conjecture,
( ( nil != sK56 )
| ( nil != sK55 ) ),
inference(cnf_transformation,[],[f509]) ).
tcf(c_249,negated_conjecture,
( ( cons(sK57,nil) = sK55 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_250,negated_conjecture,
( memberP(sK56,sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_251,negated_conjecture,
( ssItem(sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_254,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f510]) ).
tcf(c_369,negated_conjecture,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_247,c_247,c_248]) ).
tcf(c_373,negated_conjecture,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_248,c_369]) ).
tcf(c_3238,plain,
! [X0: $i,X1: $i] :
( ssItem(sK57)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK56 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_251]) ).
tcf(c_3239,plain,
( ssItem(sK57)
| ( sK56 = nil )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3238]) ).
tcf(c_3240,plain,
( ssItem(sK57)
| ( sK56 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_3239,c_254,c_141,c_3239]) ).
tcf(c_3248,plain,
! [X0: $i,X1: $i] :
( memberP(sK56,sK57)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK56 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_250]) ).
tcf(c_3249,plain,
( memberP(sK56,sK57)
| ( sK56 = nil )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3248]) ).
tcf(c_3250,plain,
( memberP(sK56,sK57)
| ( sK56 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_3249,c_254,c_141,c_3249]) ).
tcf(c_3258,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( cons(sK57,nil) = sK55 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK56 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_249]) ).
tcf(c_3259,plain,
( ( sK56 = nil )
| ( cons(sK57,nil) = sK55 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3258]) ).
tcf(c_3260,plain,
( ( sK56 = nil )
| ( cons(sK57,nil) = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_3259,c_254,c_141,c_3259]) ).
tcf(c_8893,definition,
iPr_def_10 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8894,plain,
( ( iPr_def_10 = sK55 )
| ( sK56 = nil ) ),
inference(demodulation,[status(thm)],[c_3260,c_8893]) ).
tcf(c_8895,plain,
( memberP(sK56,sK57)
| ( sK56 = nil ) ),
inference(demodulation,[status(thm)],[c_3250]) ).
tcf(c_8896,plain,
( ssItem(sK57)
| ( sK56 = nil ) ),
inference(demodulation,[status(thm)],[c_3240]) ).
tcf(c_8897,negated_conjecture,
nil != sK56,
inference(demodulation,[status(thm)],[c_373]) ).
tcf(c_8900,negated_conjecture,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(sK56,X0)
| ( cons(X0,nil) != sK55 ) ),
inference(demodulation,[status(thm)],[c_246]) ).
tcf(c_11749,plain,
( ~ ssItem(sK57)
| ~ memberP(sK56,sK57)
| ( sK55 != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_8893,c_8900]) ).
tcf(c_11791,plain,
( ( nil = sK56 )
| ~ ssItem(sK57)
| ~ memberP(sK56,sK57) ),
inference(superposition,[status(thm)],[c_8894,c_11749]) ).
tcf(c_11792,plain,
( ~ ssItem(sK57)
| ~ memberP(sK56,sK57) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11791,c_8897]) ).
tcf(c_11801,plain,
( ( nil = sK56 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_8895,c_11792]) ).
tcf(c_11802,plain,
~ ssItem(sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_11801,c_8897]) ).
tcf(c_11803,plain,
nil = sK56,
inference(backward_subsumption_resolution,[status(thm)],[c_8896,c_11802]) ).
tcf(c_11804,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11803,c_8897]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC387+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.36 % Computer : n011.cluster.edu
% 0.11/5.36 % Model : x86_64 x86_64
% 0.11/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.36 % Memory : 8046.5625MB
% 0.11/5.36 % OS : Linux 6.8.0-71-generic
% 0.11/5.36 % CPULimit : 300
% 0.11/5.36 % WCLimit : 300
% 0.11/5.36 % DateTime : Thu Sep 24 17:58:20 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.40 Running first-order theorem proving
% 0.15/5.40 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
% 0.15/5.41
% 0.15/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.41
% 0.15/5.42 % Detected problem language: tptp
% 0.15/5.43 % Proving...
% 2.61/6.07 % SZS status Started for theBenchmark.p
% 2.61/6.07 % SZS status Theorem for theBenchmark.p
% 2.61/6.07
% 2.61/6.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.61/6.07
% 2.61/6.07 % ------ iProver source info
% 2.61/6.07
% 2.61/6.07 % git: date: 2026-07-19 20:42:38 +0200
% 2.61/6.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.61/6.07 % git: non_committed_changes: false
% 2.61/6.07
% 2.61/6.07 % ------ Parsing...
% 2.61/6.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.61/6.07
% 2.61/6.07 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 2.61/6.07
% 2.61/6.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.61/6.07
% 2.61/6.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.61/6.07 % ------ Proving...
% 2.61/6.07 % ------ Problem Properties
% 2.61/6.07
% 2.61/6.07 %
% 2.61/6.07 % clauses 188
% 2.61/6.07 % conjectures 4
% 2.61/6.07 % EPR 55
% 2.61/6.07 % Horn 117
% 2.61/6.07 % unary 20
% 2.61/6.07 % binary 43
% 2.61/6.07 % lits 631
% 2.61/6.07 % lits eq 85
% 2.61/6.07 % fd_pure 0
% 2.61/6.07 % fd_pseudo 0
% 2.61/6.07 % fd_cond 21
% 2.61/6.07 % fd_pseudo_cond 14
% 2.61/6.07 % AC symbols 0
% 2.61/6.07
% 2.61/6.07 % ------ Schedule dynamic 5 is on
% 2.61/6.07
% 2.61/6.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.61/6.07
% 2.61/6.07
% 2.61/6.07 % ------
% 2.61/6.07 % Current options:
% 2.61/6.07 % ------
% 2.61/6.07
% 2.61/6.07
% 2.61/6.07 %
% 2.61/6.07
% 2.61/6.07 % ------ Proving...
% 2.61/6.07 %
% 2.61/6.07
% 2.61/6.07 % SZS status Theorem for theBenchmark.p
% 2.61/6.07
% 2.61/6.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.61/6.07
% 2.61/6.07
%------------------------------------------------------------------------------