%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC419+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 : n020.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 03:09:49 PM UTC 2026
% Result : Theorem 4.52s 1.30s
% Output : CNFRefutation 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 16 unt; 0 def)
% Number of atoms : 167 ( 63 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 199 ( 80 ~; 71 |; 36 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 48 !; 12 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( neq(X3,nil)
& ! [X7] :
( ssItem(X7)
=> ! [X8] :
( app(X8,cons(X7,nil)) != X2
| app(cons(X7,nil),X8) != X3
| ~ ssList(X8) ) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(X6,cons(X4,nil)),X5) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( neq(X3,nil)
& ! [X7] :
( ssItem(X7)
=> ! [X8] :
( app(X8,cons(X7,nil)) != X2
| app(cons(X7,nil),X8) != X3
| ~ ssList(X8) ) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(X6,cons(X4,nil)),X5) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f201,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ~ neq(X3,nil)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( app(X8,cons(X7,nil)) = X2
& app(cons(X7,nil),X8) = X3
& ssList(X8) ) ) )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(app(X6,cons(X4,nil)),X5) != X0
| app(app(X5,cons(X4,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f295,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ( ~ neq(sK56,nil)
| ( ssItem(sK57)
& sK55 = app(sK58,cons(sK57,nil))
& sK56 = app(cons(sK57,nil),sK58)
& ssList(sK58) ) )
& ( nil != sK56
| nil = sK55 )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(app(X6,cons(X4,nil)),X5) != sK53
| app(app(X5,cons(X4,nil)),X6) != sK54
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& neq(sK54,nil)
& sK53 = sK55
& sK54 = sK56
& ssList(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(X7,sK57),skolemize(X8,sK58)],[f221]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f388,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f402,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f481,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f495,plain,
ssList(sK53),
inference(cnf_transformation,[],[f295]) ).
fof(f498,plain,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f295]) ).
fof(f499,plain,
( ~ neq(sK56,nil)
| sK55 = app(sK58,cons(sK57,nil)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f500,plain,
( ~ neq(sK56,nil)
| sK56 = app(cons(sK57,nil),sK58) ),
inference(cnf_transformation,[],[f295]) ).
fof(f501,plain,
( ~ neq(sK56,nil)
| ssList(sK58) ),
inference(cnf_transformation,[],[f295]) ).
fof(f503,plain,
! [X6,X4,X5] :
( app(app(X6,cons(X4,nil)),X5) != sK53
| app(app(X5,cons(X4,nil)),X6) != sK54
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f295]) ).
fof(f504,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f295]) ).
fof(f505,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f506,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f295]) ).
fof(f508,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f504,f506]) ).
fof(f509,plain,
! [X6,X4,X5] :
( app(app(X6,cons(X4,nil)),X5) != sK55
| app(app(X5,cons(X4,nil)),X6) != sK56
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f503,f506,f505]) ).
fof(f511,plain,
ssList(sK55),
inference(definition_unfolding,[],[f495,f505]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f388]) ).
tcf(c_155,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f402]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f481]) ).
tcf(c_247,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f508]) ).
tcf(c_248,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X2,cons(X1,nil)),X0) != sK56 )
| ( app(app(X0,cons(X1,nil)),X2) != sK55 ) ),
inference(cnf_transformation,[],[f509]) ).
tcf(c_250,negated_conjecture,
( ssList(sK58)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_251,negated_conjecture,
( ( app(cons(sK57,nil),sK58) = sK56 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_252,negated_conjecture,
( ( app(sK58,cons(sK57,nil)) = sK55 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f499]) ).
tcf(c_253,negated_conjecture,
( ssItem(sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f498]) ).
tcf(c_256,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f511]) ).
tcf(c_311,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_253,c_247,c_253]) ).
tcf(c_332,plain,
app(sK55,nil) = sK55,
inference(superposition,[status(thm)],[c_256,c_232]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i] :
( ( app(nil,cons(X0,X1)) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_140,c_155]) ).
tcf(c_362,negated_conjecture,
app(sK58,cons(sK57,nil)) = sK55,
inference(global_subsumption_just,[status(thm)],[c_252,c_247,c_252]) ).
tcf(c_529,plain,
! [X0: $i] :
( ~ ssList(sK58)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ( app(sK55,X0) != sK55 )
| ( app(app(X0,cons(sK57,nil)),sK58) != sK56 ) ),
inference(superposition,[status(thm)],[c_362,c_248]) ).
tcf(c_688,plain,
! [X0: $i] :
( ( app(nil,cons(sK57,X0)) = cons(sK57,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_311,c_359]) ).
tcf(c_1086,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( app(sK55,X0) != sK55 )
| ( app(app(X0,cons(sK57,nil)),sK58) != sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_529,c_247,c_253,c_250,c_529]) ).
tcf(c_1559,plain,
app(nil,cons(sK57,nil)) = cons(sK57,nil),
inference(superposition,[status(thm)],[c_141,c_688]) ).
tcf(c_3487,plain,
( ~ ssList(nil)
| ( app(sK55,nil) != sK55 )
| ( app(cons(sK57,nil),sK58) != sK56 ) ),
inference(superposition,[status(thm)],[c_1559,c_1086]) ).
tcf(c_3489,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3487,c_332,c_251,c_247,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC419+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 18:10:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 4.52/1.30 % SZS status Started for theBenchmark.p
% 4.52/1.30 % SZS status Theorem for theBenchmark.p
% 4.52/1.30
% 4.52/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.52/1.30
% 4.52/1.30 % ------ iProver source info
% 4.52/1.30
% 4.52/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.52/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.52/1.30 % git: non_committed_changes: false
% 4.52/1.30
% 4.52/1.30 % ------ Parsing...
% 4.52/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.52/1.30 % ------ Proving...
% 4.52/1.30 % ------ Problem Properties
% 4.52/1.30
% 4.52/1.30 %
% 4.52/1.30 % clauses 208
% 4.52/1.30 % conjectures 11
% 4.52/1.30 % EPR 72
% 4.52/1.30 % Horn 137
% 4.52/1.30 % unary 17
% 4.52/1.30 % binary 58
% 4.52/1.30 % lits 690
% 4.52/1.30 % lits eq 87
% 4.52/1.30 % fd_pure 0
% 4.52/1.30 % fd_pseudo 0
% 4.52/1.30 % fd_cond 21
% 4.52/1.30 % fd_pseudo_cond 17
% 4.52/1.30 % AC symbols 0
% 4.52/1.30
% 4.52/1.30 % ------ Input Options Time Limit: Unbounded
% 4.52/1.30
% 4.52/1.30
% 4.52/1.30 % ------
% 4.52/1.30 % Current options:
% 4.52/1.30 % ------
% 4.52/1.30
% 4.52/1.30
% 4.52/1.30 %
% 4.52/1.30
% 4.52/1.30 % ------ Proving...
% 4.52/1.30 %
% 4.52/1.30
% 4.52/1.30 % SZS status Theorem for theBenchmark.p
% 4.52/1.30
% 4.52/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.52/1.30
% 4.52/1.30
%------------------------------------------------------------------------------