%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT381+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 : n007.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 01:59:45 PM UTC 2026
% Result : Theorem 2.41s 1.28s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 26 unt; 0 def)
% Number of atoms : 223 ( 30 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 290 ( 132 ~; 126 |; 23 &)
% ( 2 <=>; 7 =>; 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 : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 89 ( 0 sgn 86 !; 3 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f8,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mASymm) ).
fof(f13,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> ! [X2] :
( aSupremumOfIn0(X2,X1,X0)
<=> ( ! [X3] :
( aUpperBoundOfIn0(X3,X1,X0)
=> sdtlseqdt0(X2,X3) )
& aUpperBoundOfIn0(X2,X1,X0)
& aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSup) ).
fof(f14,axiom,
aSet0(xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__725) ).
fof(f15,axiom,
aSubsetOf0(xS,xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__725_01) ).
fof(f16,axiom,
( aSupremumOfIn0(xv,xS,xT)
& aSupremumOfIn0(xu,xS,xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__744) ).
fof(f17,conjecture,
xu = xv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f18,negated_conjecture,
xu != xv,
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f22,plain,
xu != xv,
inference(flattening,[],[f18]) ).
fof(f23,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f27,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f28,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f27]) ).
fof(f34,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| ! [X2] :
( aSupremumOfIn0(X2,X1,X0)
<=> ( ! [X3] :
( ~ aUpperBoundOfIn0(X3,X1,X0)
| sdtlseqdt0(X2,X3) )
& aUpperBoundOfIn0(X2,X1,X0)
& aElementOf0(X2,X0) ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f54,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| ! [X2] :
( ( ~ aSupremumOfIn0(X2,X1,X0)
| ( ! [X3] :
( ~ aUpperBoundOfIn0(X3,X1,X0)
| sdtlseqdt0(X2,X3) )
& aUpperBoundOfIn0(X2,X1,X0)
& aElementOf0(X2,X0) ) )
& ( ? [X3] :
( aUpperBoundOfIn0(X3,X1,X0)
& ~ sdtlseqdt0(X2,X3) )
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aSupremumOfIn0(X2,X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f55,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| ! [X2] :
( ( ~ aSupremumOfIn0(X2,X1,X0)
| ( ! [X3] :
( ~ aUpperBoundOfIn0(X3,X1,X0)
| sdtlseqdt0(X2,X3) )
& aUpperBoundOfIn0(X2,X1,X0)
& aElementOf0(X2,X0) ) )
& ( ? [X3] :
( aUpperBoundOfIn0(X3,X1,X0)
& ~ sdtlseqdt0(X2,X3) )
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aSupremumOfIn0(X2,X1,X0) ) ) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| ! [X2] :
( ( ~ aSupremumOfIn0(X2,X1,X0)
| ( ! [X4] :
( ~ aUpperBoundOfIn0(X4,X1,X0)
| sdtlseqdt0(X2,X4) )
& aUpperBoundOfIn0(X2,X1,X0)
& aElementOf0(X2,X0) ) )
& ( ? [X3] :
( aUpperBoundOfIn0(X3,X1,X0)
& ~ sdtlseqdt0(X2,X3) )
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aSupremumOfIn0(X2,X1,X0) ) ) ) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aSubsetOf0(X1,X0)
| ! [X2] :
( ( ~ aSupremumOfIn0(X2,X1,X0)
| ( ! [X4] :
( ~ aUpperBoundOfIn0(X4,X1,X0)
| sdtlseqdt0(X2,X4) )
& aUpperBoundOfIn0(X2,X1,X0)
& aElementOf0(X2,X0) ) )
& ( ( aUpperBoundOfIn0(sK5(X0,X1,X2),X1,X0)
& ~ sdtlseqdt0(X2,sK5(X0,X1,X2)) )
| ~ aUpperBoundOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| aSupremumOfIn0(X2,X1,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f66,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f28]) ).
fof(f81,plain,
! [X2,X0,X1,X4] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aUpperBoundOfIn0(X4,X1,X0)
| sdtlseqdt0(X2,X4) ),
inference(cnf_transformation,[],[f57]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| aUpperBoundOfIn0(X2,X1,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| aElementOf0(X2,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f86,plain,
aSet0(xT),
inference(cnf_transformation,[],[f14]) ).
fof(f87,plain,
aSubsetOf0(xS,xT),
inference(cnf_transformation,[],[f15]) ).
fof(f88,plain,
aSupremumOfIn0(xv,xS,xT),
inference(cnf_transformation,[],[f16]) ).
fof(f89,plain,
aSupremumOfIn0(xu,xS,xT),
inference(cnf_transformation,[],[f16]) ).
fof(f90,plain,
xu != xv,
inference(cnf_transformation,[],[f22]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSupremumOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( aUpperBoundOfIn0(X0,X1,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSupremumOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X3,X0)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSupremumOfIn0(X3,X1,X2)
| ~ aUpperBoundOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_77,plain,
aSet0(xT),
inference(cnf_transformation,[],[f86]) ).
tcf(c_78,plain,
aSubsetOf0(xS,xT),
inference(cnf_transformation,[],[f87]) ).
tcf(c_79,plain,
aSupremumOfIn0(xu,xS,xT),
inference(cnf_transformation,[],[f89]) ).
tcf(c_80,plain,
aSupremumOfIn0(xv,xS,xT),
inference(cnf_transformation,[],[f88]) ).
tcf(c_81,negated_conjecture,
xu != xv,
inference(cnf_transformation,[],[f90]) ).
tcf(c_750,plain,
! [X0: $i,X1: $i,X2: $i] :
( aUpperBoundOfIn0(X0,X1,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ( X2 != xT )
| ( X1 != xS )
| ( X0 != xu ) ),
inference(resolution_lifted,[status(thm)],[c_75,c_79]) ).
tcf(c_751,plain,
( aUpperBoundOfIn0(xu,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT) ),
inference(unflattening,[status(thm)],[c_750]) ).
tcf(c_752,plain,
aUpperBoundOfIn0(xu,xS,xT),
inference(global_subsumption_just,[status(thm)],[c_751,c_77,c_78,c_751]) ).
tcf(c_757,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ( X2 != xT )
| ( X1 != xS )
| ( X0 != xu ) ),
inference(resolution_lifted,[status(thm)],[c_74,c_79]) ).
tcf(c_758,plain,
( aElementOf0(xu,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT) ),
inference(unflattening,[status(thm)],[c_757]) ).
tcf(c_759,plain,
aElementOf0(xu,xT),
inference(global_subsumption_just,[status(thm)],[c_758,c_77,c_78,c_758]) ).
tcf(c_764,plain,
! [X0: $i,X1: $i,X2: $i] :
( aUpperBoundOfIn0(X0,X1,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ( X2 != xT )
| ( X1 != xS )
| ( X0 != xv ) ),
inference(resolution_lifted,[status(thm)],[c_75,c_80]) ).
tcf(c_765,plain,
( aUpperBoundOfIn0(xv,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT) ),
inference(unflattening,[status(thm)],[c_764]) ).
tcf(c_766,plain,
aUpperBoundOfIn0(xv,xS,xT),
inference(global_subsumption_just,[status(thm)],[c_765,c_77,c_78,c_765]) ).
tcf(c_771,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ( X2 != xT )
| ( X1 != xS )
| ( X0 != xv ) ),
inference(resolution_lifted,[status(thm)],[c_74,c_80]) ).
tcf(c_772,plain,
( aElementOf0(xv,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT) ),
inference(unflattening,[status(thm)],[c_771]) ).
tcf(c_773,plain,
aElementOf0(xv,xT),
inference(global_subsumption_just,[status(thm)],[c_772,c_77,c_78,c_772]) ).
tcf(c_778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X2,X3)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aUpperBoundOfIn0(X3,X0,X1)
| ( X2 != xu )
| ( X1 != xT )
| ( X0 != xS ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_79]) ).
tcf(c_779,plain,
! [X0: $i] :
( sdtlseqdt0(xu,X0)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| ~ aUpperBoundOfIn0(X0,xS,xT) ),
inference(unflattening,[status(thm)],[c_778]) ).
tcf(c_781,plain,
! [X0: $i] :
( sdtlseqdt0(xu,X0)
| ~ aUpperBoundOfIn0(X0,xS,xT) ),
inference(global_subsumption_just,[status(thm)],[c_779,c_77,c_78,c_779]) ).
tcf(c_790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X2,X3)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aUpperBoundOfIn0(X3,X0,X1)
| ( X2 != xv )
| ( X1 != xT )
| ( X0 != xS ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_80]) ).
tcf(c_791,plain,
! [X0: $i] :
( sdtlseqdt0(xv,X0)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT)
| ~ aUpperBoundOfIn0(X0,xS,xT) ),
inference(unflattening,[status(thm)],[c_790]) ).
tcf(c_793,plain,
! [X0: $i] :
( sdtlseqdt0(xv,X0)
| ~ aUpperBoundOfIn0(X0,xS,xT) ),
inference(global_subsumption_just,[status(thm)],[c_791,c_77,c_78,c_791]) ).
tcf(c_3109,negated_conjecture,
xu != xv,
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_3678,plain,
( aElement0(xu)
| ~ aSet0(xT) ),
inference(superposition,[status(thm)],[c_759,c_49]) ).
tcf(c_3679,plain,
( aElement0(xv)
| ~ aSet0(xT) ),
inference(superposition,[status(thm)],[c_773,c_49]) ).
tcf(c_3680,plain,
aElement0(xv),
inference(forward_subsumption_resolution,[status(thm)],[c_3679,c_77]) ).
tcf(c_3681,plain,
aElement0(xu),
inference(forward_subsumption_resolution,[status(thm)],[c_3678,c_77]) ).
tcf(c_3732,plain,
sdtlseqdt0(xu,xv),
inference(superposition,[status(thm)],[c_766,c_781]) ).
tcf(c_3734,plain,
( ( xu = xv )
| ~ aElement0(xv)
| ~ aElement0(xu)
| ~ sdtlseqdt0(xv,xu) ),
inference(superposition,[status(thm)],[c_3732,c_57]) ).
tcf(c_3735,plain,
~ sdtlseqdt0(xv,xu),
inference(forward_subsumption_resolution,[status(thm)],[c_3734,c_3109,c_3680,c_3681]) ).
tcf(c_3740,plain,
sdtlseqdt0(xv,xu),
inference(superposition,[status(thm)],[c_752,c_793]) ).
tcf(c_3742,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3740,c_3735]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT381+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 21:28:07 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 2.41/1.28 % SZS status Started for theBenchmark.p
% 2.41/1.28 % SZS status Theorem for theBenchmark.p
% 2.41/1.28
% 2.41/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.41/1.28
% 2.41/1.28 % ------ iProver source info
% 2.41/1.28
% 2.41/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.41/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.41/1.28 % git: non_committed_changes: false
% 2.41/1.28
% 2.41/1.28 % ------ Parsing...
% 2.41/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.41/1.28
% 2.41/1.28 % ------ 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: 2 0s sf_e pe_s pe_e %
% 2.41/1.28
% 2.41/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.41/1.28
% 2.41/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.41/1.28 % ------ Proving...
% 2.41/1.28 % ------ Problem Properties
% 2.41/1.28
% 2.41/1.28 %
% 2.41/1.28 % clauses 30
% 2.41/1.28 % conjectures 1
% 2.41/1.28 % EPR 19
% 2.41/1.28 % Horn 25
% 2.41/1.28 % unary 7
% 2.41/1.28 % binary 3
% 2.41/1.28 % lits 107
% 2.41/1.28 % lits eq 2
% 2.41/1.28 % fd_pure 0
% 2.41/1.28 % fd_pseudo 0
% 2.41/1.28 % fd_cond 0
% 2.41/1.28 % fd_pseudo_cond 1
% 2.41/1.28 % AC symbols 0
% 2.41/1.28
% 2.41/1.28 % ------ Schedule dynamic 5 is on
% 2.41/1.28
% 2.41/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.41/1.28
% 2.41/1.28
% 2.41/1.28 % ------
% 2.41/1.28 % Current options:
% 2.41/1.28 % ------
% 2.41/1.28
% 2.41/1.28
% 2.41/1.28 %
% 2.41/1.28
% 2.41/1.28 % ------ Proving...
% 2.41/1.28 %
% 2.41/1.28
% 2.41/1.28 % SZS status Theorem for theBenchmark.p
% 2.41/1.28
% 2.41/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.41/1.28
% 2.41/1.28
%------------------------------------------------------------------------------