%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC378+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 : n017.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 03:09:32 PM UTC 2026
% Result : Theorem 4.63s 1.42s
% Output : CNFRefutation 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 57 ( 16 unt; 0 def)
% Number of atoms : 226 ( 22 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 280 ( 111 ~; 124 |; 32 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 56 !; 7 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ! [X6] :
( ( memberP(X0,X6)
& memberP(X1,X6) )
| ( ~ memberP(X0,X6)
& ~ memberP(X1,X6) )
| ~ ssItem(X6) )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( app(X5,X4) != X2
| app(X4,X5) != X3
| ~ ssList(X5) ) )
| 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] :
( ! [X6] :
( ( memberP(X0,X6)
& memberP(X1,X6) )
| ( ~ memberP(X0,X6)
& ~ memberP(X1,X6) )
| ~ ssItem(X6) )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( app(X5,X4) != X2
| app(X4,X5) != X3
| ~ ssList(X5) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ? [X6] :
( ( ~ memberP(X0,X6)
| ~ memberP(X1,X6) )
& ( memberP(X0,X6)
| memberP(X1,X6) )
& ssItem(X6) )
& ? [X4] :
( ssList(X4)
& ? [X5] :
( app(X5,X4) = X2
& app(X4,X5) = X3
& ssList(X5) ) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f112,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f121,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ( ~ memberP(sK0,sK6)
| ~ memberP(sK1,sK6) )
& ( memberP(sK0,sK6)
| memberP(sK1,sK6) )
& ssItem(sK6)
& ssList(sK4)
& sK2 = app(sK5,sK4)
& sK3 = app(sK4,sK5)
& ssList(sK5)
& sK0 = sK2
& sK1 = sK3
& ssList(sK3) ),
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)],[f98]) ).
fof(f127,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f112]) ).
fof(f128,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(flattening,[],[f127]) ).
fof(f136,plain,
( ~ memberP(sK0,sK6)
| ~ memberP(sK1,sK6) ),
inference(cnf_transformation,[],[f121]) ).
fof(f137,plain,
( memberP(sK0,sK6)
| memberP(sK1,sK6) ),
inference(cnf_transformation,[],[f121]) ).
fof(f138,plain,
ssItem(sK6),
inference(cnf_transformation,[],[f121]) ).
fof(f139,plain,
ssList(sK4),
inference(cnf_transformation,[],[f121]) ).
fof(f140,plain,
sK2 = app(sK5,sK4),
inference(cnf_transformation,[],[f121]) ).
fof(f141,plain,
sK3 = app(sK4,sK5),
inference(cnf_transformation,[],[f121]) ).
fof(f142,plain,
ssList(sK5),
inference(cnf_transformation,[],[f121]) ).
fof(f143,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f121]) ).
fof(f144,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f121]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f165,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f180,plain,
( memberP(sK2,sK6)
| memberP(sK3,sK6) ),
inference(definition_unfolding,[],[f137,f144,f143]) ).
fof(f181,plain,
( ~ memberP(sK2,sK6)
| ~ memberP(sK3,sK6) ),
inference(definition_unfolding,[],[f136,f144,f143]) ).
tcf(c_50,negated_conjecture,
ssList(sK5),
inference(cnf_transformation,[],[f142]) ).
tcf(c_51,negated_conjecture,
app(sK4,sK5) = sK3,
inference(cnf_transformation,[],[f141]) ).
tcf(c_52,negated_conjecture,
app(sK5,sK4) = sK2,
inference(cnf_transformation,[],[f140]) ).
tcf(c_53,negated_conjecture,
ssList(sK4),
inference(cnf_transformation,[],[f139]) ).
tcf(c_54,negated_conjecture,
ssItem(sK6),
inference(cnf_transformation,[],[f138]) ).
tcf(c_55,negated_conjecture,
( memberP(sK2,sK6)
| memberP(sK3,sK6) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_56,negated_conjecture,
( ~ memberP(sK2,sK6)
| ~ memberP(sK3,sK6) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| memberP(X0,X2)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ memberP(app(X0,X1),X2) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_2574,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssList(sK4)
| ~ ssList(sK5)
| ~ ssItem(X0)
| ~ memberP(sK4,X0) ),
inference(superposition,[status(thm)],[c_51,c_78]) ).
tcf(c_2575,plain,
! [X0: $i] :
( memberP(sK2,X0)
| ~ ssList(sK4)
| ~ ssList(sK5)
| ~ ssItem(X0)
| ~ memberP(sK5,X0) ),
inference(superposition,[status(thm)],[c_52,c_78]) ).
tcf(c_2585,plain,
! [X0: $i] :
( memberP(sK2,X0)
| ~ ssItem(X0)
| ~ memberP(sK5,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2575,c_53,c_50]) ).
tcf(c_2589,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK4,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2574,c_53,c_50]) ).
tcf(c_2743,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssList(sK4)
| ~ ssList(sK5)
| ~ ssItem(X0)
| ~ memberP(sK5,X0) ),
inference(superposition,[status(thm)],[c_51,c_79]) ).
tcf(c_2744,plain,
! [X0: $i] :
( memberP(sK2,X0)
| ~ ssList(sK4)
| ~ ssList(sK5)
| ~ ssItem(X0)
| ~ memberP(sK4,X0) ),
inference(superposition,[status(thm)],[c_52,c_79]) ).
tcf(c_2761,plain,
! [X0: $i] :
( memberP(sK2,X0)
| ~ ssItem(X0)
| ~ memberP(sK4,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2744,c_53,c_50]) ).
tcf(c_2765,plain,
! [X0: $i] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK5,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2743,c_53,c_50]) ).
tcf(c_2946,plain,
! [X0: $i] :
( memberP(sK4,X0)
| memberP(sK5,X0)
| ~ ssList(sK4)
| ~ ssList(sK5)
| ~ ssItem(X0)
| ~ memberP(sK3,X0) ),
inference(superposition,[status(thm)],[c_51,c_80]) ).
tcf(c_2947,plain,
! [X0: $i] :
( memberP(sK4,X0)
| memberP(sK5,X0)
| ~ ssList(sK4)
| ~ ssList(sK5)
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(superposition,[status(thm)],[c_52,c_80]) ).
tcf(c_2964,plain,
! [X0: $i] :
( memberP(sK4,X0)
| memberP(sK5,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2947,c_53,c_50]) ).
tcf(c_2969,plain,
! [X0: $i] :
( memberP(sK4,X0)
| memberP(sK5,X0)
| ~ ssItem(X0)
| ~ memberP(sK3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2946,c_53,c_50]) ).
tcf(c_5016,plain,
( memberP(sK4,sK6)
| memberP(sK5,sK6)
| memberP(sK3,sK6)
| ~ ssItem(sK6) ),
inference(superposition,[status(thm)],[c_55,c_2964]) ).
tcf(c_5017,plain,
( memberP(sK4,sK6)
| memberP(sK5,sK6)
| memberP(sK3,sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5016,c_54]) ).
tcf(c_5029,plain,
( memberP(sK5,sK6)
| memberP(sK3,sK6)
| ~ ssItem(sK6) ),
inference(superposition,[status(thm)],[c_5017,c_2589]) ).
tcf(c_5030,plain,
( memberP(sK5,sK6)
| memberP(sK3,sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5029,c_54]) ).
tcf(c_5038,plain,
( memberP(sK3,sK6)
| ~ ssItem(sK6) ),
inference(superposition,[status(thm)],[c_5030,c_2765]) ).
tcf(c_5040,plain,
memberP(sK3,sK6),
inference(forward_subsumption_resolution,[status(thm)],[c_5038,c_54]) ).
tcf(c_5041,plain,
~ memberP(sK2,sK6),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_5040]) ).
tcf(c_5607,plain,
( memberP(sK4,sK6)
| memberP(sK5,sK6)
| ~ ssItem(sK6) ),
inference(superposition,[status(thm)],[c_5040,c_2969]) ).
tcf(c_5608,plain,
( memberP(sK4,sK6)
| memberP(sK5,sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5607,c_54]) ).
tcf(c_5616,plain,
( memberP(sK2,sK6)
| memberP(sK5,sK6)
| ~ ssItem(sK6) ),
inference(superposition,[status(thm)],[c_5608,c_2761]) ).
tcf(c_5618,plain,
memberP(sK5,sK6),
inference(forward_subsumption_resolution,[status(thm)],[c_5616,c_5041,c_54]) ).
tcf(c_5621,plain,
( memberP(sK2,sK6)
| ~ ssItem(sK6) ),
inference(superposition,[status(thm)],[c_5618,c_2585]) ).
tcf(c_5622,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5621,c_5041,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC378+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.43 % Computer : n017.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Thu Sep 24 17:51:01 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.49 Running first-order theorem proving
% 0.18/0.49 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
% 0.25/0.51
% 0.25/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.51
% 0.25/0.51 % Detected problem language: tptp
% 0.25/0.53 % Proving...
% 4.63/1.42 % SZS status Started for theBenchmark.p
% 4.63/1.42 % SZS status Theorem for theBenchmark.p
% 4.63/1.42
% 4.63/1.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.63/1.42
% 4.63/1.42 % ------ iProver source info
% 4.63/1.42
% 4.63/1.42 % git: date: 2026-07-19 20:42:38 +0200
% 4.63/1.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.63/1.42 % git: non_committed_changes: false
% 4.63/1.42
% 4.63/1.42 % ------ Parsing...
% 4.63/1.42 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.63/1.42
% 4.63/1.42 % ------ 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 %
% 4.63/1.42
% 4.63/1.42 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.63/1.42
% 4.63/1.42 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.63/1.42 % ------ Proving...
% 4.63/1.42 % ------ Problem Properties
% 4.63/1.42
% 4.63/1.42 %
% 4.63/1.42 % clauses 43
% 4.63/1.42 % conjectures 9
% 4.63/1.42 % EPR 12
% 4.63/1.42 % Horn 37
% 4.63/1.42 % unary 12
% 4.63/1.42 % binary 5
% 4.63/1.42 % lits 131
% 4.63/1.42 % lits eq 29
% 4.63/1.42 % fd_pure 0
% 4.63/1.42 % fd_pseudo 0
% 4.63/1.42 % fd_cond 4
% 4.63/1.42 % fd_pseudo_cond 5
% 4.63/1.42 % AC symbols 0
% 4.63/1.42
% 4.63/1.42 % ------ Schedule dynamic 5 is on
% 4.63/1.42
% 4.63/1.42 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.63/1.42
% 4.63/1.42
% 4.63/1.42 % ------
% 4.63/1.42 % Current options:
% 4.63/1.42 % ------
% 4.63/1.42
% 4.63/1.42
% 4.63/1.42 %
% 4.63/1.42
% 4.63/1.42 % ------ Proving...
% 4.63/1.42 %
% 4.63/1.42
% 4.63/1.42 % SZS status Theorem for theBenchmark.p
% 4.63/1.42
% 4.63/1.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.63/1.42
%------------------------------------------------------------------------------