%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC408+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 : n002.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 03:09:40 PM UTC 2026
% Result : Theorem 3.84s 1.27s
% Output : CNFRefutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 23 unt; 1 def)
% Number of atoms : 128 ( 21 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 131 ( 46 ~; 39 |; 31 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 30 !; 10 ?; 5 :)
% 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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X4] :
( ssItem(X4)
=> ( memberP(X0,X4)
| ~ memberP(X1,X4) ) )
| X0 != X2
| X1 != X3
| app(X3,X3) != 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)
=> ( memberP(X0,X4)
| ~ memberP(X1,X4) ) )
| X0 != X2
| X1 != X3
| app(X3,X3) != X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f146,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(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssItem(X4)
& ~ memberP(X0,X4)
& memberP(X1,X4) )
& X0 = X2
& X1 = X3
& app(X3,X3) = X2 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssItem(X4)
& ~ memberP(X0,X4)
& memberP(X1,X4) )
& X0 = X2
& X1 = X3
& app(X3,X3) = X2 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f277,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,[],[f146]) ).
fof(f278,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,[],[f277]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ssItem(sK57)
& ~ memberP(sK53,sK57)
& memberP(sK54,sK57)
& sK53 = sK55
& sK54 = sK56
& sK55 = app(sK56,sK56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57)],[f222]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
~ memberP(sK53,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
memberP(sK54,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK55 = app(sK56,sK56),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
memberP(sK56,sK57),
inference(definition_unfolding,[],[f502,f504]) ).
fof(f507,plain,
~ memberP(sK55,sK57),
inference(definition_unfolding,[],[f501,f503]) ).
fof(f508,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f504]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f415]) ).
tcf(c_246,negated_conjecture,
app(sK56,sK56) = sK55,
inference(cnf_transformation,[],[f505]) ).
tcf(c_247,negated_conjecture,
memberP(sK56,sK57),
inference(cnf_transformation,[],[f506]) ).
tcf(c_248,negated_conjecture,
~ memberP(sK55,sK57),
inference(cnf_transformation,[],[f507]) ).
tcf(c_249,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f500]) ).
tcf(c_252,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f508]) ).
tcf(c_8783,definition,
iPr_def_10 = app(sK56,sK56),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8785,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_252]) ).
tcf(c_8786,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_249]) ).
tcf(c_8787,negated_conjecture,
~ memberP(sK55,sK57),
inference(demodulation,[status(thm)],[c_248]) ).
tcf(c_8788,negated_conjecture,
memberP(sK56,sK57),
inference(demodulation,[status(thm)],[c_247]) ).
tcf(c_8789,negated_conjecture,
iPr_def_10 = sK55,
inference(demodulation,[status(thm)],[c_246,c_8783]) ).
tcf(c_11594,plain,
~ memberP(iPr_def_10,sK57),
inference(light_normalisation,[status(thm)],[c_8787,c_8789]) ).
tcf(c_16927,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssList(sK56)
| ~ ssItem(X0)
| ~ memberP(sK56,X0) ),
inference(superposition,[status(thm)],[c_8783,c_165]) ).
tcf(c_16953,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssItem(X0)
| ~ memberP(sK56,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16927,c_8785]) ).
tcf(c_17372,plain,
( memberP(iPr_def_10,sK57)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_8788,c_16953]) ).
tcf(c_17373,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_17372,c_11594,c_8786]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC408+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 18:07:49 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 3.84/1.27 % SZS status Started for theBenchmark.p
% 3.84/1.27 % SZS status Theorem for theBenchmark.p
% 3.84/1.27
% 3.84/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.84/1.27
% 3.84/1.27 % ------ iProver source info
% 3.84/1.27
% 3.84/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.84/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.84/1.27 % git: non_committed_changes: false
% 3.84/1.27
% 3.84/1.27 % ------ Parsing...
% 3.84/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.84/1.27
% 3.84/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 3.84/1.27
% 3.84/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.84/1.27
% 3.84/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.84/1.27 % ------ Proving...
% 3.84/1.27 % ------ Problem Properties
% 3.84/1.27
% 3.84/1.27 %
% 3.84/1.27 % clauses 187
% 3.84/1.27 % conjectures 6
% 3.84/1.27 % EPR 55
% 3.84/1.27 % Horn 119
% 3.84/1.27 % unary 23
% 3.84/1.27 % binary 40
% 3.84/1.27 % lits 625
% 3.84/1.27 % lits eq 80
% 3.84/1.27 % fd_pure 0
% 3.84/1.27 % fd_pseudo 0
% 3.84/1.27 % fd_cond 21
% 3.84/1.27 % fd_pseudo_cond 14
% 3.84/1.27 % AC symbols 0
% 3.84/1.27
% 3.84/1.27 % ------ Schedule dynamic 5 is on
% 3.84/1.27
% 3.84/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.84/1.27
% 3.84/1.27
% 3.84/1.27 % ------
% 3.84/1.27 % Current options:
% 3.84/1.27 % ------
% 3.84/1.27
% 3.84/1.27
% 3.84/1.27 %
% 3.84/1.27
% 3.84/1.27 % ------ Proving...
% 3.84/1.27 %
% 3.84/1.27
% 3.84/1.27 % SZS status Theorem for theBenchmark.p
% 3.84/1.27
% 3.84/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.84/1.27
% 3.84/1.27
%------------------------------------------------------------------------------