%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC049+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 : n003.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 03:07:40 PM UTC 2026
% Result : Theorem 2.68s 1.21s
% Output : CNFRefutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 62 ( 19 unt; 0 def)
% Number of atoms : 240 ( 66 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 299 ( 121 ~; 108 |; 51 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 58 !; 14 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
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(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ~ rearsegP(X3,X2)
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X0
& nil = X1 )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( rearsegP(X0,X4)
& rearsegP(X1,X4)
& neq(X4,nil)
& ssList(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)
=> ( ( ( ~ rearsegP(X3,X2)
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X0
& nil = X1 )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( rearsegP(X0,X4)
& rearsegP(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)
& ( ( rearsegP(X3,X2)
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X0
| nil != X1 )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ~ rearsegP(X0,X4)
| ~ rearsegP(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)
& ( ( rearsegP(X3,X2)
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X0
| nil != X1 )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ~ rearsegP(X0,X4)
| ~ rearsegP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f114,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f128,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f129,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f130,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( rearsegP(sK3,sK2)
& neq(sK2,nil) )
| ~ neq(sK3,nil) )
& ( nil != sK0
| nil != sK1 )
& ( nil != sK3
| nil = sK2 )
& ! [X4] :
( ~ rearsegP(sK0,X4)
| ~ rearsegP(sK1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f136,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ rearsegP(X0,X1)
| ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
& ( ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) )
| rearsegP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f114]) ).
fof(f137,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ rearsegP(X0,X1)
| ? [X3] :
( app(X3,X1) = X0
& ssList(X3) ) )
& ( ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) )
| rearsegP(X0,X1) ) ) ) ),
inference(rectify,[],[f136]) ).
fof(f138,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ rearsegP(X0,X1)
| ( app(sK8(X0,X1),X1) = X0
& ssList(sK8(X0,X1)) ) )
& ( ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) )
| rearsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1))],[f137]) ).
fof(f141,plain,
ssList(sK0),
inference(cnf_transformation,[],[f130]) ).
fof(f142,plain,
ssList(sK1),
inference(cnf_transformation,[],[f130]) ).
fof(f145,plain,
( rearsegP(sK3,sK2)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f130]) ).
fof(f146,plain,
( neq(sK2,nil)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f130]) ).
fof(f147,plain,
( nil != sK0
| nil != sK1 ),
inference(cnf_transformation,[],[f130]) ).
fof(f148,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f130]) ).
fof(f149,plain,
! [X4] :
( ~ rearsegP(sK0,X4)
| ~ rearsegP(sK1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f130]) ).
fof(f150,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f130]) ).
fof(f151,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f130]) ).
fof(f156,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f163,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f173,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f187,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f128]) ).
fof(f188,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f189,plain,
! [X4] :
( ~ rearsegP(sK2,X4)
| ~ rearsegP(sK3,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f149,f151,f150]) ).
fof(f190,plain,
( nil != sK2
| nil != sK3 ),
inference(definition_unfolding,[],[f147,f151,f150]) ).
fof(f191,plain,
ssList(sK3),
inference(definition_unfolding,[],[f142,f151]) ).
fof(f192,plain,
ssList(sK2),
inference(definition_unfolding,[],[f141,f150]) ).
fof(f196,plain,
! [X2,X1] :
( ~ ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X2,X1),X1) ),
inference(equality_resolution,[],[f173]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ rearsegP(sK2,X0)
| ~ rearsegP(sK3,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_50,negated_conjecture,
( ( nil = sK2 )
| ( nil != sK3 ) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_51,negated_conjecture,
( ( nil != sK2 )
| ( nil != sK3 ) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_52,negated_conjecture,
( neq(sK2,nil)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_53,negated_conjecture,
( rearsegP(sK3,sK2)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_56,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f191]) ).
tcf(c_57,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f192]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_69,plain,
ssList(nil),
inference(cnf_transformation,[],[f163]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_93,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_120,negated_conjecture,
nil != sK3,
inference(global_subsumption_just,[status(thm)],[c_50,c_50,c_51]) ).
tcf(c_124,negated_conjecture,
nil != sK3,
inference(global_subsumption_just,[status(thm)],[c_51,c_120]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_77,c_94,c_77]) ).
tcf(c_1808,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_57,c_93]) ).
tcf(c_1855,plain,
( rearsegP(sK2,sK2)
| ~ ssList(sK2)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_1808,c_126]) ).
tcf(c_1856,plain,
rearsegP(sK2,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_1855,c_57,c_69]) ).
tcf(c_1899,plain,
( rearsegP(sK3,sK2)
| ( nil = sK3 )
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_61,c_53]) ).
tcf(c_1900,plain,
( neq(sK2,nil)
| ( nil = sK3 )
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_61,c_52]) ).
tcf(c_1903,plain,
neq(sK2,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_1900,c_124,c_56,c_69]) ).
tcf(c_1904,plain,
rearsegP(sK3,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_1899,c_124,c_56,c_69]) ).
tcf(c_1927,plain,
( ~ ssList(sK2)
| ~ rearsegP(sK2,sK2)
| ~ rearsegP(sK3,sK2) ),
inference(superposition,[status(thm)],[c_1903,c_49]) ).
tcf(c_1928,plain,
~ rearsegP(sK3,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_1927,c_57,c_1856]) ).
tcf(c_1929,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1928,c_1904]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC049+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 16:07:36 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 2.68/1.21 % SZS status Started for theBenchmark.p
% 2.68/1.21 % SZS status Theorem for theBenchmark.p
% 2.68/1.21
% 2.68/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.68/1.21
% 2.68/1.21 % ------ iProver source info
% 2.68/1.21
% 2.68/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 2.68/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.68/1.21 % git: non_committed_changes: false
% 2.68/1.21
% 2.68/1.21 % ------ Parsing...
% 2.68/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.68/1.21
% 2.68/1.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.68/1.21
% 2.68/1.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.68/1.21
% 2.68/1.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.68/1.21 % ------ Proving...
% 2.68/1.21 % ------ Problem Properties
% 2.68/1.21
% 2.68/1.21 %
% 2.68/1.21 % clauses 43
% 2.68/1.21 % conjectures 6
% 2.68/1.21 % EPR 20
% 2.68/1.21 % Horn 38
% 2.68/1.21 % unary 9
% 2.68/1.21 % binary 8
% 2.68/1.21 % lits 129
% 2.68/1.21 % lits eq 31
% 2.68/1.21 % fd_pure 0
% 2.68/1.21 % fd_pseudo 0
% 2.68/1.21 % fd_cond 5
% 2.68/1.21 % fd_pseudo_cond 7
% 2.68/1.21 % AC symbols 0
% 2.68/1.21
% 2.68/1.21 % ------ Schedule dynamic 5 is on
% 2.68/1.21
% 2.68/1.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.68/1.21
% 2.68/1.21
% 2.68/1.21 % ------
% 2.68/1.21 % Current options:
% 2.68/1.21 % ------
% 2.68/1.21
% 2.68/1.21
% 2.68/1.21 %
% 2.68/1.21
% 2.68/1.21 % ------ Proving...
% 2.68/1.21 %
% 2.68/1.21
% 2.68/1.21 % SZS status Theorem for theBenchmark.p
% 2.68/1.21
% 2.68/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.68/1.21
% 2.68/1.21
%------------------------------------------------------------------------------