%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC050+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 2.53s 1.30s
% Output : CNFRefutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 43 ( 9 unt; 1 def)
% Number of atoms : 213 ( 36 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 274 ( 104 ~; 94 |; 66 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 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 : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 97 !; 19 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X5] :
( ssList(X5)
=> ( ~ rearsegP(X2,X5)
| ~ rearsegP(X3,X5)
| ~ neq(X5,nil) ) )
| ? [X4] :
( rearsegP(X0,X4)
& rearsegP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) ) )
| 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)
| ~ neq(X1,nil) )
& ( ! [X5] :
( ssList(X5)
=> ( ~ rearsegP(X2,X5)
| ~ rearsegP(X3,X5)
| ~ neq(X5,nil) ) )
| ? [X4] :
( rearsegP(X0,X4)
& rearsegP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X5] :
( ssList(X5)
& rearsegP(X2,X5)
& rearsegP(X3,X5)
& neq(X5,nil) )
& ! [X4] :
( ~ rearsegP(X0,X4)
| ~ rearsegP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) ) )
& 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)
& neq(X1,nil) )
| ( ? [X5] :
( ssList(X5)
& rearsegP(X2,X5)
& rearsegP(X3,X5)
& neq(X5,nil) )
& ! [X4] :
( ~ rearsegP(X0,X4)
| ~ rearsegP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f301,plain,
( ssList(sK55)
& ssList(sK56)
& ssList(sK57)
& ssList(sK58)
& ( ( ~ neq(sK58,nil)
& neq(sK56,nil) )
| sP6(sK56,sK55,sK58,sK57) )
& sK55 = sK57
& sK56 = sK58 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55,sK56,sK57,sK58]),skolemize(X0,sK55),skolemize(X1,sK56),skolemize(X2,sK57),skolemize(X3,sK58)],[f233]) ).
fof(f511,plain,
( ~ neq(sK58,nil)
| sP6(sK56,sK55,sK58,sK57) ),
inference(cnf_transformation,[],[f301]) ).
fof(f512,plain,
( neq(sK56,nil)
| sP6(sK56,sK55,sK58,sK57) ),
inference(cnf_transformation,[],[f301]) ).
fof(f513,plain,
sK55 = sK57,
inference(cnf_transformation,[],[f301]) ).
fof(f514,plain,
sK56 = sK58,
inference(cnf_transformation,[],[f301]) ).
fof(f515,plain,
( neq(sK58,nil)
| sP6(sK58,sK57,sK58,sK57) ),
inference(definition_unfolding,[],[f512,f514,f513,f514]) ).
fof(f516,plain,
( ~ neq(sK58,nil)
| sP6(sK58,sK57,sK58,sK57) ),
inference(definition_unfolding,[],[f511,f514,f513]) ).
tcf(c_252,negated_conjecture,
( neq(sK58,nil)
| sP6(sK58,sK57,sK58,sK57) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_253,negated_conjecture,
( sP6(sK58,sK57,sK58,sK57)
| ~ neq(sK58,nil) ),
inference(cnf_transformation,[],[f516]) ).
tcf(c_375,negated_conjecture,
sP6(sK58,sK57,sK58,sK57),
inference(global_subsumption_just,[status(thm)],[c_252,c_252,c_253]) ).
tcf(c_377,negated_conjecture,
sP6(sK58,sK57,sK58,sK57),
inference(global_subsumption_just,[status(thm)],[c_253,c_375]) ).
fof(f232,definition,
! [X1,X0,X3,X2] :
( ~ sP6(X1,X0,X3,X2)
| ( ? [X5] :
( ssList(X5)
& rearsegP(X2,X5)
& rearsegP(X3,X5)
& neq(X5,nil) )
& ! [X4] :
( ~ rearsegP(X0,X4)
| ~ rearsegP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f233,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X1,X0,X3,X2) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f222,f232]) ).
fof(f298,plain,
! [X1,X0,X3,X2] :
( ~ sP6(X1,X0,X3,X2)
| ( ? [X5] :
( ssList(X5)
& rearsegP(X2,X5)
& rearsegP(X3,X5)
& neq(X5,nil) )
& ! [X4] :
( ~ rearsegP(X0,X4)
| ~ rearsegP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f299,plain,
! [X0,X1,X2,X3] :
( ~ sP6(X0,X1,X2,X3)
| ( ? [X5] :
( ssList(X5)
& rearsegP(X3,X5)
& rearsegP(X2,X5)
& neq(X5,nil) )
& ! [X4] :
( ~ rearsegP(X1,X4)
| ~ rearsegP(X0,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X0,nil) ) ),
inference(rectify,[],[f298]) ).
fof(f300,plain,
! [X0,X1,X2,X3] :
( ~ sP6(X0,X1,X2,X3)
| ( ssList(sK54(X2,X3))
& rearsegP(X3,sK54(X2,X3))
& rearsegP(X2,sK54(X2,X3))
& neq(sK54(X2,X3),nil)
& ! [X4] :
( ~ rearsegP(X1,X4)
| ~ rearsegP(X0,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X0,nil) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(X5,sK54(X2,X3))],[f299]) ).
fof(f501,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| ssList(sK54(X2,X3)) ),
inference(cnf_transformation,[],[f300]) ).
fof(f502,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| rearsegP(X3,sK54(X2,X3)) ),
inference(cnf_transformation,[],[f300]) ).
fof(f503,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| rearsegP(X2,sK54(X2,X3)) ),
inference(cnf_transformation,[],[f300]) ).
fof(f504,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| neq(sK54(X2,X3),nil) ),
inference(cnf_transformation,[],[f300]) ).
fof(f505,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP6(X0,X1,X2,X3)
| ~ rearsegP(X1,X4)
| ~ rearsegP(X0,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f300]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ rearsegP(X1,X4)
| ~ rearsegP(X0,X4)
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( neq(sK54(X2,X3),nil)
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( rearsegP(X2,sK54(X2,X3))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( rearsegP(X3,sK54(X2,X3))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK54(X2,X3))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_3217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK54(X2,X3))
| ( X3 != sK57 )
| ( X2 != sK58 )
| ( X1 != sK57 )
| ( X0 != sK58 ) ),
inference(resolution_lifted,[status(thm)],[c_251,c_377]) ).
tcf(c_3218,plain,
ssList(sK54(sK58,sK57)),
inference(unflattening,[status(thm)],[c_3217]) ).
tcf(c_3222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( rearsegP(X3,sK54(X2,X3))
| ( X3 != sK57 )
| ( X2 != sK58 )
| ( X1 != sK57 )
| ( X0 != sK58 ) ),
inference(resolution_lifted,[status(thm)],[c_250,c_377]) ).
tcf(c_3223,plain,
rearsegP(sK57,sK54(sK58,sK57)),
inference(unflattening,[status(thm)],[c_3222]) ).
tcf(c_3227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( rearsegP(X2,sK54(X2,X3))
| ( X3 != sK57 )
| ( X2 != sK58 )
| ( X1 != sK57 )
| ( X0 != sK58 ) ),
inference(resolution_lifted,[status(thm)],[c_249,c_377]) ).
tcf(c_3228,plain,
rearsegP(sK58,sK54(sK58,sK57)),
inference(unflattening,[status(thm)],[c_3227]) ).
tcf(c_3232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( neq(sK54(X2,X3),nil)
| ( X3 != sK57 )
| ( X2 != sK58 )
| ( X1 != sK57 )
| ( X0 != sK58 ) ),
inference(resolution_lifted,[status(thm)],[c_248,c_377]) ).
tcf(c_3233,plain,
neq(sK54(sK58,sK57),nil),
inference(unflattening,[status(thm)],[c_3232]) ).
tcf(c_3237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ rearsegP(X1,X4)
| ~ rearsegP(X0,X4)
| ( X3 != sK57 )
| ( X2 != sK58 )
| ( X1 != sK57 )
| ( X0 != sK58 ) ),
inference(resolution_lifted,[status(thm)],[c_247,c_377]) ).
tcf(c_3238,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ rearsegP(sK57,X0)
| ~ rearsegP(sK58,X0)
| ~ neq(X0,nil) ),
inference(unflattening,[status(thm)],[c_3237]) ).
tcf(c_3367,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ rearsegP(sK57,X0)
| ~ rearsegP(sK58,X0)
| ( nil != nil )
| ( sK54(sK58,sK57) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_3238,c_3233]) ).
tcf(c_3368,plain,
( ~ ssList(sK54(sK58,sK57))
| ~ rearsegP(sK57,sK54(sK58,sK57))
| ~ rearsegP(sK58,sK54(sK58,sK57)) ),
inference(unflattening,[status(thm)],[c_3367]) ).
tcf(c_3369,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3368,c_3228,c_3223,c_3218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC050+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n003.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 16:07:51 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 2.53/1.30 % SZS status Started for theBenchmark.p
% 2.53/1.30 % SZS status Theorem for theBenchmark.p
% 2.53/1.30
% 2.53/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.53/1.30
% 2.53/1.30 % ------ iProver source info
% 2.53/1.30
% 2.53/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.53/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.53/1.30 % git: non_committed_changes: false
% 2.53/1.30
% 2.53/1.30 % ------ Parsing...
% 2.53/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.53/1.30
% 2.53/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s%
% 2.53/1.30
% 2.53/1.30 % SZS status Theorem for theBenchmark.p
% 2.53/1.30
% 2.53/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.53/1.30
% 2.53/1.30
%------------------------------------------------------------------------------