%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC182+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 : n007.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 03:08:18 PM UTC 2026
% Result : Theorem 1.17s 1.30s
% Output : CNFRefutation 4.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 18 unt; 0 def)
% Number of atoms : 240 ( 63 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 287 ( 107 ~; 99 |; 54 &)
% ( 4 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 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 : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 76 !; 22 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ( ~ memberP(X6,X4)
& ~ memberP(X5,X4) )
| app(app(X5,cons(X4,nil)),X6) != X0 ) ) ) )
| X0 != X2
| X1 != X3
| nil != X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ( ~ memberP(X6,X4)
& ~ memberP(X5,X4) )
| app(app(X5,cons(X4,nil)),X6) != X0 ) ) ) )
| X0 != X2
| X1 != X3
| nil != X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ( memberP(X6,X4)
| memberP(X5,X4) )
& app(app(X5,cons(X4,nil)),X6) = X0 ) ) )
& X0 = X2
& X1 = X3
& nil = X2 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ( memberP(X6,X4)
| memberP(X5,X4) )
& app(app(X5,cons(X4,nil)),X6) = X0 ) ) )
& X0 = X2
& X1 = X3
& nil = X2 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f110,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f117,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f118,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f121,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f122,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ssItem(sK4)
& ssList(sK5)
& ssList(sK6)
& ( memberP(sK6,sK4)
| memberP(sK5,sK4) )
& sK0 = app(app(sK5,cons(sK4,nil)),sK6)
& sK0 = sK2
& sK1 = sK3
& nil = sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f99]) ).
fof(f125,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f110]) ).
fof(f126,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(flattening,[],[f125]) ).
fof(f131,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f121]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(rectify,[],[f131]) ).
fof(f133,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ( app(sK11(X0,X1),cons(X1,sK12(X0,X1))) = X0
& ssList(sK12(X0,X1))
& ssList(sK11(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X4,sK11(X0,X1)),skolemize(X5,sK12(X0,X1))],[f132]) ).
fof(f138,plain,
ssItem(sK4),
inference(cnf_transformation,[],[f122]) ).
fof(f139,plain,
ssList(sK5),
inference(cnf_transformation,[],[f122]) ).
fof(f140,plain,
ssList(sK6),
inference(cnf_transformation,[],[f122]) ).
fof(f142,plain,
sK0 = app(app(sK5,cons(sK4,nil)),sK6),
inference(cnf_transformation,[],[f122]) ).
fof(f143,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f122]) ).
fof(f145,plain,
nil = sK2,
inference(cnf_transformation,[],[f122]) ).
fof(f158,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f160,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X0 ),
inference(cnf_transformation,[],[f126]) ).
fof(f167,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f168,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f169,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f179,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f180,plain,
sK2 = app(app(sK5,cons(sK4,sK2)),sK6),
inference(definition_unfolding,[],[f142,f143,f145]) ).
fof(f191,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != sK2
| sK2 = X0 ),
inference(definition_unfolding,[],[f160,f145,f145]) ).
fof(f193,plain,
ssList(sK2),
inference(definition_unfolding,[],[f168,f145]) ).
fof(f194,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(definition_unfolding,[],[f169,f145]) ).
fof(f198,plain,
! [X2,X3,X1] :
( ~ ssList(app(X2,cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(app(X2,cons(X1,X3)),X1) ),
inference(equality_resolution,[],[f179]) ).
tcf(c_49,negated_conjecture,
app(app(sK5,cons(sK4,sK2)),sK6) = sK2,
inference(cnf_transformation,[],[f180]) ).
tcf(c_51,negated_conjecture,
ssList(sK6),
inference(cnf_transformation,[],[f140]) ).
tcf(c_52,negated_conjecture,
ssList(sK5),
inference(cnf_transformation,[],[f139]) ).
tcf(c_53,negated_conjecture,
ssItem(sK4),
inference(cnf_transformation,[],[f138]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_74,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X0 = sK2 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != sK2 ) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_80,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f193]) ).
tcf(c_81,negated_conjecture,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,cons(X1,X2)),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_1822,plain,
( ( app(sK5,cons(sK4,sK2)) = sK2 )
| ~ ssList(sK6)
| ~ ssList(app(sK5,cons(sK4,sK2))) ),
inference(superposition,[status(thm)],[c_49,c_74]) ).
tcf(c_1827,plain,
( ( app(sK5,cons(sK4,sK2)) = sK2 )
| ~ ssList(app(sK5,cons(sK4,sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1822,c_51]) ).
tcf(c_2047,plain,
( ~ ssItem(sK4)
| ~ memberP(sK2,sK4) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_2184,plain,
! [X0: $i] :
( ssList(cons(sK4,X0))
| ~ ssItem(sK4)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_2185,plain,
( ssList(cons(sK4,sK2))
| ~ ssItem(sK4)
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_2184]) ).
tcf(c_4476,plain,
( ( app(sK5,cons(sK4,sK2)) = sK2 )
| ~ ssList(sK5)
| ~ ssList(cons(sK4,sK2)) ),
inference(superposition,[status(thm)],[c_79,c_1827]) ).
tcf(c_4477,plain,
( ( app(sK5,cons(sK4,sK2)) = sK2 )
| ~ ssList(cons(sK4,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4476,c_52]) ).
tcf(c_4510,plain,
app(sK5,cons(sK4,sK2)) = sK2,
inference(global_subsumption_just,[status(thm)],[c_4477,c_80,c_53,c_2185,c_4477]) ).
tcf(c_4524,plain,
( memberP(sK2,sK4)
| ~ ssItem(sK4)
| ~ ssList(sK5)
| ~ ssList(sK2)
| ~ ssList(app(sK5,cons(sK4,sK2))) ),
inference(superposition,[status(thm)],[c_4510,c_88]) ).
tcf(c_4537,plain,
( memberP(sK2,sK4)
| ~ ssItem(sK4)
| ~ ssList(sK5)
| ~ ssList(sK2) ),
inference(light_normalisation,[status(thm)],[c_4524,c_4510]) ).
tcf(c_4538,plain,
memberP(sK2,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_4537,c_53,c_52,c_80]) ).
tcf(c_4554,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4538,c_2047,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC182+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n007.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 16:48:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 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...
% 1.17/1.30 % SZS status Started for theBenchmark.p
% 1.17/1.30 % SZS status Theorem for theBenchmark.p
% 1.17/1.30
% 1.17/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.17/1.30
% 1.17/1.30 % ------ iProver source info
% 1.17/1.30
% 1.17/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 1.17/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.17/1.30 % git: non_committed_changes: false
% 1.17/1.30
% 1.17/1.30 % ------ Parsing...
% 1.17/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.17/1.30
% 1.17/1.30 % ------ 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 %
% 1.17/1.30
% 1.17/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.17/1.30
% 1.17/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.17/1.30 % ------ Proving...
% 1.17/1.30 % ------ Problem Properties
% 1.17/1.30
% 1.17/1.30 %
% 1.17/1.30 % clauses 40
% 1.17/1.30 % conjectures 18
% 1.17/1.30 % EPR 10
% 1.17/1.30 % Horn 34
% 1.17/1.30 % unary 10
% 1.17/1.30 % binary 4
% 1.17/1.30 % lits 127
% 4.36/1.30 % lits eq 28
% 4.36/1.30 % fd_pure 0
% 4.36/1.30 % fd_pseudo 0
% 4.36/1.30 % fd_cond 4
% 4.36/1.30 % fd_pseudo_cond 5
% 4.36/1.30 % AC symbols 0
% 4.36/1.30
% 4.36/1.30 % ------ Schedule dynamic 5 is on
% 4.36/1.30
% 4.36/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.36/1.30
% 4.36/1.30
% 4.36/1.30 % ------
% 4.36/1.30 % Current options:
% 4.36/1.30 % ------
% 4.36/1.30
% 4.36/1.30
% 4.36/1.30 %
% 4.36/1.30
% 4.36/1.30 % ------ Proving...
% 4.36/1.30 %
% 4.36/1.30
% 4.36/1.30 % SZS status Theorem for theBenchmark.p
% 4.36/1.30
% 4.36/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.36/1.30
% 4.36/1.30
%------------------------------------------------------------------------------