%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM017+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 01:04:19 PM UTC 2026
% Result : Theorem 3.82s 1.28s
% Output : CNFRefutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 18 unt; 2 def)
% Number of atoms : 250 ( 1 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 331 ( 143 ~; 133 |; 48 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 87 ( 0 sgn 73 !; 14 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0] :
( aRewritingSystem0(X0)
=> ( isLocallyConfluent0(X0)
<=> ! [X1,X2,X3] :
( ( aReductOfIn0(X3,X1,X0)
& aReductOfIn0(X2,X1,X0)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mWCRDef) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
fof(f16,axiom,
( isTerminating0(xR)
& isLocallyConfluent0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656_01) ).
fof(f17,axiom,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
fof(f20,axiom,
( sdtmndtasgtdt0(xu,xR,xb)
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__755) ).
fof(f21,axiom,
( sdtmndtasgtdt0(xv,xR,xc)
& aReductOfIn0(xv,xa,xR)
& aElement0(xv) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__779) ).
fof(f22,conjecture,
? [X0] :
( sdtmndtasgtdt0(xv,xR,X0)
& sdtmndtasgtdt0(xu,xR,X0)
& aElement0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f23,negated_conjecture,
~ ? [X0] :
( sdtmndtasgtdt0(xv,xR,X0)
& sdtmndtasgtdt0(xu,xR,X0)
& aElement0(X0) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f40,plain,
! [X0] :
( ~ aRewritingSystem0(X0)
| ( isLocallyConfluent0(X0)
<=> ! [X1,X2,X3] :
( ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) ) ) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f41,plain,
! [X0] :
( ~ aRewritingSystem0(X0)
| ( isLocallyConfluent0(X0)
<=> ! [X1,X2,X3] :
( ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) ) ) ) ),
inference(flattening,[],[f40]) ).
fof(f50,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f67,plain,
! [X0] :
( ~ sP3(X0)
| ( ( ~ isLocallyConfluent0(X0)
| sP2(X0) )
& ( ~ sP2(X0)
| isLocallyConfluent0(X0) ) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f103,plain,
! [X0] :
( ~ sP3(X0)
| ~ isLocallyConfluent0(X0)
| sP2(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f114,plain,
! [X0] :
( ~ aRewritingSystem0(X0)
| sP3(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f125,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f127,plain,
isLocallyConfluent0(xR),
inference(cnf_transformation,[],[f16]) ).
fof(f130,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f137,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f20]) ).
fof(f138,plain,
aElement0(xu),
inference(cnf_transformation,[],[f20]) ).
fof(f140,plain,
aReductOfIn0(xv,xa,xR),
inference(cnf_transformation,[],[f21]) ).
fof(f141,plain,
aElement0(xv),
inference(cnf_transformation,[],[f21]) ).
fof(f142,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_73,plain,
! [X0: $i] :
( sP2(X0)
| ~ sP3(X0)
| ~ isLocallyConfluent0(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_83,plain,
! [X0: $i] :
( sP3(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_94,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f125]) ).
tcf(c_95,plain,
isLocallyConfluent0(xR),
inference(cnf_transformation,[],[f127]) ).
tcf(c_97,plain,
aElement0(xa),
inference(cnf_transformation,[],[f130]) ).
tcf(c_105,plain,
aElement0(xu),
inference(cnf_transformation,[],[f138]) ).
tcf(c_106,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f137]) ).
tcf(c_108,plain,
aElement0(xv),
inference(cnf_transformation,[],[f141]) ).
tcf(c_109,plain,
aReductOfIn0(xv,xa,xR),
inference(cnf_transformation,[],[f140]) ).
tcf(c_111,negated_conjecture,
! [X0: $i] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ sdtmndtasgtdt0(xu,xR,X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_112,plain,
( sP3(xR)
| ~ aRewritingSystem0(xR) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_122,plain,
( sP2(xR)
| ~ sP3(xR)
| ~ isLocallyConfluent0(xR) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_1032,plain,
! [X0: $i] :
( sP2(X0)
| ~ sP3(X0)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_95]) ).
tcf(c_1033,plain,
( sP2(xR)
| ~ sP3(xR) ),
inference(unflattening,[status(thm)],[c_1032]) ).
tcf(c_1034,plain,
sP2(xR),
inference(global_subsumption_just,[status(thm)],[c_1033,c_95,c_94,c_112,c_122]) ).
tcf(c_4756,negated_conjecture,
! [X0: $i] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ sdtmndtasgtdt0(xu,xR,X0) ),
inference(demodulation,[status(thm)],[c_111]) ).
fof(f54,definition,
! [X0] :
( sP2(X0)
<=> ! [X1,X2,X3] :
( ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f55,definition,
! [X0] :
( ~ sP3(X0)
| ( isLocallyConfluent0(X0)
<=> sP2(X0) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f56,plain,
! [X0] :
( ~ aRewritingSystem0(X0)
| sP3(X0) ),
inference(definition_folding,[],[f41,f55,f54]) ).
fof(f68,plain,
! [X0] :
( ( ~ sP2(X0)
| ! [X1,X2,X3] :
( ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) ) ) )
& ( ? [X1,X2,X3] :
( aReductOfIn0(X3,X1,X0)
& aReductOfIn0(X2,X1,X0)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1)
& ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) ) )
| sP2(X0) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f69,plain,
! [X0] :
( ( ~ sP2(X0)
| ! [X5,X6,X7] :
( ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ? [X8] :
( sdtmndtasgtdt0(X7,X0,X8)
& sdtmndtasgtdt0(X6,X0,X8)
& aElement0(X8) ) ) )
& ( ? [X1,X2,X3] :
( aReductOfIn0(X3,X1,X0)
& aReductOfIn0(X2,X1,X0)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1)
& ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) ) )
| sP2(X0) ) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ( ~ sP2(X0)
| ! [X5,X6,X7] :
( ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ( sdtmndtasgtdt0(X7,X0,sK12(X0,X6,X7))
& sdtmndtasgtdt0(X6,X0,sK12(X0,X6,X7))
& aElement0(sK12(X0,X6,X7)) ) ) )
& ( ( aReductOfIn0(sK11(X0),sK9(X0),X0)
& aReductOfIn0(sK10(X0),sK9(X0),X0)
& aElement0(sK11(X0))
& aElement0(sK10(X0))
& aElement0(sK9(X0))
& ! [X4] :
( ~ sdtmndtasgtdt0(sK11(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK10(X0),X0,X4)
| ~ aElement0(X4) ) )
| sP2(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X1,sK9(X0)),skolemize(X2,sK10(X0)),skolemize(X3,sK11(X0)),skolemize(X8,sK12(X0,X6,X7))],[f69]) ).
fof(f105,plain,
! [X0,X6,X7,X5] :
( ~ sP2(X0)
| ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| sdtmndtasgtdt0(X7,X0,sK12(X0,X6,X7)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f106,plain,
! [X0,X6,X7,X5] :
( ~ sP2(X0)
| ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| sdtmndtasgtdt0(X6,X0,sK12(X0,X6,X7)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f107,plain,
! [X0,X6,X7,X5] :
( ~ sP2(X0)
| ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| aElement0(sK12(X0,X6,X7)) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElement0(sK12(X2,X0,X3))
| ~ sP2(X2)
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X3,X1,X2)
| ~ aReductOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtasgtdt0(X0,X2,sK12(X2,X0,X3))
| ~ sP2(X2)
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X3,X1,X2)
| ~ aReductOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtasgtdt0(X3,X2,sK12(X2,X0,X3))
| ~ sP2(X2)
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X3,X1,X2)
| ~ aReductOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_5866,plain,
! [X0: $i] :
( aElement0(sK12(xR,xv,X0))
| ~ sP2(xR)
| ~ aElement0(xv)
| ~ aElement0(xa)
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR) ),
inference(superposition,[status(thm)],[c_109,c_80]) ).
tcf(c_5867,plain,
! [X0: $i] :
( aElement0(sK12(xR,xv,X0))
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5866,c_1034,c_108,c_97]) ).
tcf(c_6197,plain,
! [X0: $i] :
( sdtmndtasgtdt0(xv,xR,sK12(xR,xv,X0))
| ~ sP2(xR)
| ~ aElement0(xv)
| ~ aElement0(xa)
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR) ),
inference(superposition,[status(thm)],[c_109,c_81]) ).
tcf(c_6198,plain,
! [X0: $i] :
( sdtmndtasgtdt0(xv,xR,sK12(xR,xv,X0))
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6197,c_1034,c_108,c_97]) ).
tcf(c_6226,plain,
! [X0: $i] :
( sdtmndtasgtdt0(X0,xR,sK12(xR,xv,X0))
| ~ sP2(xR)
| ~ aElement0(xv)
| ~ aElement0(xa)
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR) ),
inference(superposition,[status(thm)],[c_109,c_82]) ).
tcf(c_6227,plain,
! [X0: $i] :
( sdtmndtasgtdt0(X0,xR,sK12(xR,xv,X0))
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6226,c_1034,c_108,c_97]) ).
tcf(c_6365,plain,
( ~ aElement0(xu)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aElement0(sK12(xR,xv,xu))
| ~ sdtmndtasgtdt0(xv,xR,sK12(xR,xv,xu)) ),
inference(superposition,[status(thm)],[c_6227,c_4756]) ).
tcf(c_6366,plain,
( ~ aElement0(sK12(xR,xv,xu))
| ~ sdtmndtasgtdt0(xv,xR,sK12(xR,xv,xu)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6365,c_105,c_106]) ).
tcf(c_6409,plain,
( ~ aElement0(xu)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aElement0(sK12(xR,xv,xu)) ),
inference(superposition,[status(thm)],[c_6198,c_6366]) ).
tcf(c_6410,plain,
~ aElement0(sK12(xR,xv,xu)),
inference(forward_subsumption_resolution,[status(thm)],[c_6409,c_105,c_106]) ).
tcf(c_6411,plain,
( ~ aElement0(xu)
| ~ aReductOfIn0(xu,xa,xR) ),
inference(superposition,[status(thm)],[c_5867,c_6410]) ).
tcf(c_6412,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6411,c_105,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM017+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n026.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 07:50:09 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.82/1.28 % SZS status Started for theBenchmark.p
% 3.82/1.28 % SZS status Theorem for theBenchmark.p
% 3.82/1.28
% 3.82/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.82/1.28
% 3.82/1.28 % ------ iProver source info
% 3.82/1.28
% 3.82/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.82/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.82/1.28 % git: non_committed_changes: false
% 3.82/1.28
% 3.82/1.28 % ------ Parsing...
% 3.82/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.82/1.28
% 3.82/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e %
% 3.82/1.28
% 3.82/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.82/1.28
% 3.82/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.82/1.28 % ------ Proving...
% 3.82/1.28 % ------ Problem Properties
% 3.82/1.28
% 3.82/1.28 %
% 3.82/1.28 % clauses 49
% 3.82/1.28 % conjectures 1
% 3.82/1.28 % EPR 21
% 3.82/1.28 % Horn 35
% 3.82/1.28 % unary 12
% 3.82/1.28 % binary 14
% 3.82/1.28 % lits 166
% 3.82/1.28 % lits eq 1
% 3.82/1.28 % fd_pure 0
% 3.82/1.28 % fd_pseudo 0
% 3.82/1.28 % fd_cond 0
% 3.82/1.28 % fd_pseudo_cond 1
% 3.82/1.28 % AC symbols 0
% 3.82/1.28
% 3.82/1.28 % ------ Schedule dynamic 5 is on
% 3.82/1.28
% 3.82/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.82/1.28
% 3.82/1.28
% 3.82/1.28 % ------
% 3.82/1.28 % Current options:
% 3.82/1.28 % ------
% 3.82/1.28
% 3.82/1.28
% 3.82/1.28 %
% 3.82/1.28
% 3.82/1.28 % ------ Proving...
% 3.82/1.28 %
% 3.82/1.28
% 3.82/1.28 % SZS status Theorem for theBenchmark.p
% 3.82/1.28
% 3.82/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.82/1.28
% 3.82/1.28
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