%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM012+3 : 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 : n010.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 1.79s 1.16s
% Output : CNFRefutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 48 ( 24 unt; 0 def)
% Number of atoms : 247 ( 34 equ)
% Maximal formula atoms : 21 ( 5 avg)
% Number of connectives : 284 ( 85 ~; 98 |; 96 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 48 ( 0 sgn 33 !; 15 ?; 13 :)
% 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(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)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xz)
& aReductOfIn0(X0,xy,xR)
& aElement0(X0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xy)
& aReductOfIn0(X0,xx,xR)
& aElement0(X0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) )
=> ( sdtmndtasgtdt0(xx,xR,xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ? [X0] :
( sdtmndtplgtdt0(X0,xR,xz)
& aReductOfIn0(X0,xx,xR)
& aElement0(X0) )
| aReductOfIn0(xz,xx,xR)
| xx = xz ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f11,negated_conjecture,
~ ( ( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xz)
& aReductOfIn0(X0,xy,xR)
& aElement0(X0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xy)
& aReductOfIn0(X0,xx,xR)
& aElement0(X0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) )
=> ( sdtmndtasgtdt0(xx,xR,xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ? [X0] :
( sdtmndtplgtdt0(X0,xR,xz)
& aReductOfIn0(X0,xx,xR)
& aElement0(X0) )
| aReductOfIn0(xz,xx,xR)
| xx = xz ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f16,plain,
~ ( ( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xz)
& aReductOfIn0(X1,xy,xR)
& aElement0(X1) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xy)
& aReductOfIn0(X0,xx,xR)
& aElement0(X0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) )
=> ( sdtmndtasgtdt0(xx,xR,xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,xz)
& aReductOfIn0(X2,xx,xR)
& aElement0(X2) )
| aReductOfIn0(xz,xx,xR)
| xx = xz ) ),
inference(rectify,[],[f11]) ).
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(ennf_transformation,[],[f7]) ).
fof(f22,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,[],[f21]) ).
fof(f25,plain,
( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xz)
& aReductOfIn0(X1,xy,xR)
& aElement0(X1) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xy)
& aReductOfIn0(X0,xx,xR)
& aElement0(X0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy )
& ~ sdtmndtasgtdt0(xx,xR,xz)
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,xz)
| ~ aReductOfIn0(X2,xx,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(xz,xx,xR)
& xx != xz ),
inference(ennf_transformation,[],[f16]) ).
fof(f26,plain,
( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xz)
& aReductOfIn0(X1,xy,xR)
& aElement0(X1) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xy)
& aReductOfIn0(X0,xx,xR)
& aElement0(X0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy )
& ~ sdtmndtasgtdt0(xx,xR,xz)
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,xz)
| ~ aReductOfIn0(X2,xx,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(xz,xx,xR)
& xx != xz ),
inference(flattening,[],[f25]) ).
fof(f33,plain,
( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [X2] :
( sdtmndtplgtdt0(X2,xR,xz)
& aReductOfIn0(X2,xy,xR)
& aElement0(X2) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xy)
& aReductOfIn0(X1,xx,xR)
& aElement0(X1) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy )
& ~ sdtmndtasgtdt0(xx,xR,xz)
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ! [X0] :
( ~ sdtmndtplgtdt0(X0,xR,xz)
| ~ aReductOfIn0(X0,xx,xR)
| ~ aElement0(X0) )
& ~ aReductOfIn0(xz,xx,xR)
& xx != xz ),
inference(rectify,[],[f26]) ).
fof(f34,plain,
( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(sK2,xR,xz)
& aReductOfIn0(sK2,xy,xR)
& aElement0(sK2) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(sK1,xR,xy)
& aReductOfIn0(sK1,xx,xR)
& aElement0(sK1) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy )
& ~ sdtmndtasgtdt0(xx,xR,xz)
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ! [X0] :
( ~ sdtmndtplgtdt0(X0,xR,xz)
| ~ aReductOfIn0(X0,xx,xR)
| ~ aElement0(X0) )
& ~ aReductOfIn0(xz,xx,xR)
& xx != xz ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1),skolemize(X2,sK2)],[f33]) ).
fof(f41,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,[],[f22]) ).
fof(f45,plain,
aElement0(xz),
inference(cnf_transformation,[],[f9]) ).
fof(f46,plain,
aElement0(xy),
inference(cnf_transformation,[],[f9]) ).
fof(f47,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f9]) ).
fof(f48,plain,
aElement0(xx),
inference(cnf_transformation,[],[f9]) ).
fof(f49,plain,
sdtmndtasgtdt0(xy,xR,xz),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| xy = xz ),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
sdtmndtasgtdt0(xx,xR,xy),
inference(cnf_transformation,[],[f34]) ).
fof(f55,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy ),
inference(cnf_transformation,[],[f34]) ).
fof(f59,plain,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(cnf_transformation,[],[f34]) ).
fof(f60,plain,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(cnf_transformation,[],[f34]) ).
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,[],[f41]) ).
tcf(c_59,plain,
aElement0(xx),
inference(cnf_transformation,[],[f48]) ).
tcf(c_60,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f47]) ).
tcf(c_61,plain,
aElement0(xy),
inference(cnf_transformation,[],[f46]) ).
tcf(c_62,plain,
aElement0(xz),
inference(cnf_transformation,[],[f45]) ).
tcf(c_66,negated_conjecture,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(cnf_transformation,[],[f60]) ).
tcf(c_67,negated_conjecture,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(cnf_transformation,[],[f59]) ).
tcf(c_71,negated_conjecture,
( sdtmndtplgtdt0(xx,xR,xy)
| ( xx = xy ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_72,negated_conjecture,
sdtmndtasgtdt0(xx,xR,xy),
inference(cnf_transformation,[],[f54]) ).
tcf(c_76,negated_conjecture,
( sdtmndtplgtdt0(xy,xR,xz)
| ( xy = xz ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_77,negated_conjecture,
sdtmndtasgtdt0(xy,xR,xz),
inference(cnf_transformation,[],[f49]) ).
tcf(c_439,plain,
( ( xy != xz )
| ( xR != xR )
| ( xx != xx ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_72]) ).
tcf(c_449,plain,
( ( xz != xz )
| ( xR != xR )
| ( xx != xy ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_77]) ).
tcf(c_505,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_506,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_505]) ).
tcf(c_611,plain,
xx != xy,
inference(equality_resolution_simp,[status(thm)],[c_449]) ).
tcf(c_612,plain,
xy != xz,
inference(equality_resolution_simp,[status(thm)],[c_439]) ).
tcf(c_613,negated_conjecture,
sdtmndtplgtdt0(xy,xR,xz),
inference(global_subsumption_just,[status(thm)],[c_76,c_76,c_612]) ).
tcf(c_621,negated_conjecture,
sdtmndtplgtdt0(xx,xR,xy),
inference(global_subsumption_just,[status(thm)],[c_71,c_71,c_611]) ).
tcf(c_827,negated_conjecture,
sdtmndtplgtdt0(xx,xR,xy),
inference(demodulation,[status(thm)],[c_621]) ).
tcf(c_831,negated_conjecture,
sdtmndtplgtdt0(xy,xR,xz),
inference(demodulation,[status(thm)],[c_613]) ).
tcf(c_834,negated_conjecture,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_1262,plain,
! [X0: $i] :
( sdtmndtplgtdt0(X0,xR,xz)
| ~ aElement0(xz)
| ~ aElement0(xy)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,xy) ),
inference(superposition,[status(thm)],[c_831,c_506]) ).
tcf(c_1268,plain,
! [X0: $i] :
( sdtmndtplgtdt0(X0,xR,xz)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,xy) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1262,c_62,c_61]) ).
tcf(c_1290,plain,
( sdtmndtplgtdt0(xx,xR,xz)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_827,c_1268]) ).
tcf(c_1291,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1290,c_834,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM012+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 07:46:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 1.79/1.16 % SZS status Started for theBenchmark.p
% 1.79/1.16 % SZS status Theorem for theBenchmark.p
% 1.79/1.16
% 1.79/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.79/1.16
% 1.79/1.16 % ------ iProver source info
% 1.79/1.16
% 1.79/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 1.79/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.79/1.16 % git: non_committed_changes: false
% 1.79/1.16
% 1.79/1.16 % ------ Parsing...
% 1.79/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.79/1.16
% 1.79/1.16 % ------ 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 %
% 1.79/1.16
% 1.79/1.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.79/1.16
% 1.79/1.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.79/1.16 % ------ Proving...
% 1.79/1.16 % ------ Problem Properties
% 1.79/1.16
% 1.79/1.16 %
% 1.79/1.16 % clauses 24
% 1.79/1.16 % conjectures 12
% 1.79/1.16 % EPR 21
% 1.79/1.16 % Horn 18
% 1.79/1.16 % unary 13
% 1.79/1.16 % binary 3
% 1.79/1.16 % lits 54
% 1.79/1.16 % lits eq 3
% 1.79/1.16 % fd_pure 0
% 1.79/1.16 % fd_pseudo 0
% 1.79/1.16 % fd_cond 0
% 1.79/1.16 % fd_pseudo_cond 0
% 1.79/1.16 % AC symbols 0
% 1.79/1.16
% 1.79/1.16 % ------ Schedule dynamic 5 is on
% 1.79/1.16
% 1.79/1.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.79/1.16
% 1.79/1.16
% 1.79/1.16 % ------
% 1.79/1.16 % Current options:
% 1.79/1.16 % ------
% 1.79/1.16
% 1.79/1.16
% 1.79/1.16 %
% 1.79/1.16
% 1.79/1.16 % ------ Proving...
% 1.79/1.16 %
% 1.79/1.16
% 1.79/1.16 % SZS status Theorem for theBenchmark.p
% 1.79/1.16
% 1.79/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.79/1.16
% 1.79/1.16
%------------------------------------------------------------------------------