%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM012+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 01:04:18 PM UTC 2026
% Result : Theorem 1.67s 1.29s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 57 ( 23 unt; 0 def)
% Number of atoms : 202 ( 33 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 265 ( 120 ~; 118 |; 19 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 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; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 65 ( 0 sgn 65 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1,X2,X3] :
( ( aElement0(X3)
& aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( ( sdtmndtplgtdt0(X2,X1,X3)
& sdtmndtplgtdt0(X0,X1,X2) )
=> sdtmndtplgtdt0(X0,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCTrans) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCRDef) ).
fof(f9,axiom,
( aElement0(xz)
& aElement0(xy)
& aRewritingSystem0(xR)
& aElement0(xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__349) ).
fof(f10,conjecture,
( ( sdtmndtasgtdt0(xy,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy) )
=> sdtmndtasgtdt0(xx,xR,xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f11,negated_conjecture,
~ ( ( sdtmndtasgtdt0(xy,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy) )
=> sdtmndtasgtdt0(xx,xR,xz) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X3) ),
inference(ennf_transformation,[],[f7]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X3) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
( sdtmndtasgtdt0(xy,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy)
& ~ sdtmndtasgtdt0(xx,xR,xz) ),
inference(ennf_transformation,[],[f11]) ).
fof(f25,plain,
( sdtmndtasgtdt0(xy,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy)
& ~ sdtmndtasgtdt0(xx,xR,xz) ),
inference(flattening,[],[f24]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( ( ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 )
& ( ( ~ sdtmndtplgtdt0(X0,X1,X2)
& X0 != X2 )
| sdtmndtasgtdt0(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( ( ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 )
& ( ( ~ sdtmndtplgtdt0(X0,X1,X2)
& X0 != X2 )
| sdtmndtasgtdt0(X0,X1,X2) ) ) ),
inference(flattening,[],[f30]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ),
inference(cnf_transformation,[],[f31]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f42,plain,
aElement0(xz),
inference(cnf_transformation,[],[f9]) ).
fof(f43,plain,
aElement0(xy),
inference(cnf_transformation,[],[f9]) ).
fof(f44,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f9]) ).
fof(f45,plain,
aElement0(xx),
inference(cnf_transformation,[],[f9]) ).
fof(f46,plain,
sdtmndtasgtdt0(xy,xR,xz),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
sdtmndtasgtdt0(xx,xR,xy),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(cnf_transformation,[],[f25]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtplgtdt0(X3,X1,X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X3,X1,X0)
| ~ sdtmndtplgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X0,X1,X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtplgtdt0(X0,X1,X2)
| ( X0 = X2 )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_59,plain,
aElement0(xx),
inference(cnf_transformation,[],[f45]) ).
tcf(c_60,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f44]) ).
tcf(c_61,plain,
aElement0(xy),
inference(cnf_transformation,[],[f43]) ).
tcf(c_62,plain,
aElement0(xz),
inference(cnf_transformation,[],[f42]) ).
tcf(c_63,negated_conjecture,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(cnf_transformation,[],[f48]) ).
tcf(c_64,negated_conjecture,
sdtmndtasgtdt0(xx,xR,xy),
inference(cnf_transformation,[],[f47]) ).
tcf(c_65,negated_conjecture,
sdtmndtasgtdt0(xy,xR,xz),
inference(cnf_transformation,[],[f46]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ( X2 != xz )
| ( X1 != xR )
| ( X0 != xx ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_63]) ).
tcf(c_319,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(xz)
| ~ aElement0(xx)
| ~ sdtmndtplgtdt0(xx,xR,xz) ),
inference(unflattening,[status(thm)],[c_318]) ).
tcf(c_320,plain,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(global_subsumption_just,[status(thm)],[c_319,c_62,c_60,c_59,c_319]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtplgtdt0(X0,X1,X2)
| ( X0 = X2 )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ( X2 != xy )
| ( X1 != xR )
| ( X0 != xx ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_64]) ).
tcf(c_326,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| ( xx = xy )
| ~ aRewritingSystem0(xR)
| ~ aElement0(xy)
| ~ aElement0(xx) ),
inference(unflattening,[status(thm)],[c_325]) ).
tcf(c_327,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| ( xx = xy ) ),
inference(global_subsumption_just,[status(thm)],[c_326,c_61,c_60,c_59,c_326]) ).
tcf(c_335,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtplgtdt0(X0,X1,X2)
| ( X0 = X2 )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ( X2 != xz )
| ( X1 != xR )
| ( X0 != xy ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_65]) ).
tcf(c_336,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| ( xy = xz )
| ~ aRewritingSystem0(xR)
| ~ aElement0(xz)
| ~ aElement0(xy) ),
inference(unflattening,[status(thm)],[c_335]) ).
tcf(c_337,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| ( xy = xz ) ),
inference(global_subsumption_just,[status(thm)],[c_336,c_62,c_61,c_60,c_336]) ).
tcf(c_345,plain,
( ( xy != xz )
| ( xR != xR )
| ( xx != xx ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_64]) ).
tcf(c_355,plain,
( ( xz != xz )
| ( xR != xR )
| ( xx != xy ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_65]) ).
tcf(c_417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtplgtdt0(X3,X0,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(X3,X0,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_60]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtplgtdt0(X2,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ sdtmndtplgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_417]) ).
tcf(c_523,plain,
xx != xy,
inference(equality_resolution_simp,[status(thm)],[c_355]) ).
tcf(c_524,plain,
xy != xz,
inference(equality_resolution_simp,[status(thm)],[c_345]) ).
tcf(c_525,plain,
sdtmndtplgtdt0(xy,xR,xz),
inference(global_subsumption_just,[status(thm)],[c_337,c_337,c_524]) ).
tcf(c_527,plain,
sdtmndtplgtdt0(xx,xR,xy),
inference(global_subsumption_just,[status(thm)],[c_327,c_327,c_523]) ).
tcf(c_679,plain,
sdtmndtplgtdt0(xx,xR,xy),
inference(demodulation,[status(thm)],[c_527]) ).
tcf(c_680,plain,
sdtmndtplgtdt0(xy,xR,xz),
inference(demodulation,[status(thm)],[c_525]) ).
tcf(c_683,plain,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(demodulation,[status(thm)],[c_320]) ).
tcf(c_1021,plain,
! [X0: $i] :
( sdtmndtplgtdt0(X0,xR,xz)
| ~ aElement0(xz)
| ~ aElement0(xy)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,xy) ),
inference(superposition,[status(thm)],[c_680,c_418]) ).
tcf(c_1024,plain,
! [X0: $i] :
( sdtmndtplgtdt0(X0,xR,xz)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,xy) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1021,c_62,c_61]) ).
tcf(c_1057,plain,
( sdtmndtplgtdt0(xx,xR,xz)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_679,c_1024]) ).
tcf(c_1059,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1057,c_683,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM012+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 07:49:09 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.67/1.29 % SZS status Started for theBenchmark.p
% 1.67/1.29 % SZS status Theorem for theBenchmark.p
% 1.67/1.29
% 1.67/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.67/1.29
% 1.67/1.29 % ------ iProver source info
% 1.67/1.29
% 1.67/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.67/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.67/1.29 % git: non_committed_changes: false
% 1.67/1.29
% 1.67/1.29 % ------ Parsing...
% 1.67/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.67/1.29
% 1.67/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 1.67/1.29
% 1.67/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.67/1.29
% 1.67/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.67/1.29 % ------ Proving...
% 1.67/1.29 % ------ Problem Properties
% 1.67/1.29
% 1.67/1.29 %
% 1.67/1.29 % clauses 16
% 1.67/1.29 % conjectures 0
% 1.67/1.29 % EPR 13
% 1.67/1.29 % Horn 13
% 1.67/1.29 % unary 9
% 1.67/1.29 % binary 0
% 1.67/1.29 % lits 41
% 1.67/1.29 % lits eq 3
% 1.67/1.29 % fd_pure 0
% 1.67/1.29 % fd_pseudo 0
% 1.67/1.29 % fd_cond 0
% 1.67/1.29 % fd_pseudo_cond 0
% 1.67/1.29 % AC symbols 0
% 1.67/1.29
% 1.67/1.29 % ------ Schedule dynamic 5 is on
% 1.67/1.29
% 1.67/1.29 % ------ no conjectures: strip conj schedule
% 1.67/1.29
% 1.67/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.67/1.29
% 1.67/1.29
% 1.67/1.29 % ------
% 1.67/1.29 % Current options:
% 1.67/1.29 % ------
% 1.67/1.29
% 1.67/1.29
% 1.67/1.29 %
% 1.67/1.29
% 1.67/1.29 % ------ Proving...
% 1.67/1.29 %
% 1.67/1.29
% 1.67/1.29 % SZS status Theorem for theBenchmark.p
% 1.67/1.29
% 1.67/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.67/1.29
% 1.67/1.29
%------------------------------------------------------------------------------