%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG088+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.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 02:38:48 PM UTC 2026
% Result : Theorem 3.31s 1.29s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 13 unt; 2 def)
% Number of atoms : 99 ( 4 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 89 ( 28 ~; 22 |; 27 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 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 : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
( aIdeal0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) )
& ! [X1] :
( aElementOf0(X1,xJ)
=> aElementOf0(sdtpldt0(X0,X1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
fof(f27,axiom,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__934) ).
fof(f28,axiom,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__967) ).
fof(f29,conjecture,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f30,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f35,plain,
( aIdeal0(xJ)
& ! [X3] :
( aElementOf0(X3,xJ)
=> ( ! [X5] :
( aElement0(X5)
=> aElementOf0(sdtasdt0(X5,X3),xJ) )
& ! [X4] :
( aElementOf0(X4,xJ)
=> aElementOf0(sdtpldt0(X3,X4),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(rectify,[],[f25]) ).
fof(f68,plain,
( aIdeal0(xJ)
& ! [X3] :
( ~ aElementOf0(X3,xJ)
| ( ! [X5] :
( ~ aElement0(X5)
| aElementOf0(sdtasdt0(X5,X3),xJ) )
& ! [X4] :
( ~ aElementOf0(X4,xJ)
| aElementOf0(sdtpldt0(X3,X4),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X0] :
( ~ aElementOf0(X0,xI)
| ( ! [X2] :
( ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(ennf_transformation,[],[f35]) ).
fof(f69,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(ennf_transformation,[],[f30]) ).
fof(f137,plain,
! [X3,X4] :
( ~ aElementOf0(X3,xJ)
| ~ aElementOf0(X4,xJ)
| aElementOf0(sdtpldt0(X3,X4),xJ) ),
inference(cnf_transformation,[],[f68]) ).
fof(f141,plain,
! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ),
inference(cnf_transformation,[],[f68]) ).
fof(f153,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f27]) ).
fof(f154,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f27]) ).
fof(f156,plain,
aElementOf0(xn,xJ),
inference(cnf_transformation,[],[f28]) ).
fof(f157,plain,
aElementOf0(xm,xI),
inference(cnf_transformation,[],[f28]) ).
fof(f158,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtpldt0(X1,X0),xJ)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xJ) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_116,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f154]) ).
tcf(c_117,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_119,plain,
aElementOf0(xm,xI),
inference(cnf_transformation,[],[f157]) ).
tcf(c_120,plain,
aElementOf0(xn,xJ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_122,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_2941,definition,
iPr_def_10 = sdtpldt0(xk,xm),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2942,definition,
iPr_def_11 = sdtpldt0(xl,xn),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2943,negated_conjecture,
( ~ aElementOf0(iPr_def_11,xJ)
| ~ aElementOf0(iPr_def_10,xI) ),
inference(demodulation,[status(thm)],[c_122,c_2942,c_2941]) ).
tcf(c_4579,plain,
( aElementOf0(iPr_def_10,xI)
| ~ aElementOf0(xm,xI)
| ~ aElementOf0(xk,xI) ),
inference(superposition,[status(thm)],[c_2941,c_100]) ).
tcf(c_4594,plain,
aElementOf0(iPr_def_10,xI),
inference(forward_subsumption_resolution,[status(thm)],[c_4579,c_119,c_116]) ).
tcf(c_4611,plain,
~ aElementOf0(iPr_def_11,xJ),
inference(backward_subsumption_resolution,[status(thm)],[c_2943,c_4594]) ).
tcf(c_4694,plain,
( aElementOf0(iPr_def_11,xJ)
| ~ aElementOf0(xn,xJ)
| ~ aElementOf0(xl,xJ) ),
inference(superposition,[status(thm)],[c_2942,c_104]) ).
tcf(c_4707,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4694,c_4611,c_120,c_117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG088+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 08:10:49 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 3.31/1.29 % SZS status Started for theBenchmark.p
% 3.31/1.29 % SZS status Theorem for theBenchmark.p
% 3.31/1.29
% 3.31/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.31/1.29
% 3.31/1.29 % ------ iProver source info
% 3.31/1.29
% 3.31/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 3.31/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.31/1.29 % git: non_committed_changes: false
% 3.31/1.29
% 3.31/1.29 % ------ Parsing...
% 3.31/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.31/1.29
% 3.31/1.29 % ------ 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: 2 0s sf_e pe_s pe_e %
% 3.31/1.29
% 3.31/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.31/1.29
% 3.31/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.31/1.29 % ------ Proving...
% 3.31/1.29 % ------ Problem Properties
% 3.31/1.29
% 3.31/1.29 %
% 3.31/1.29 % clauses 70
% 3.31/1.29 % conjectures 1
% 3.31/1.29 % EPR 17
% 3.31/1.29 % Horn 61
% 3.31/1.29 % unary 22
% 3.31/1.29 % binary 13
% 3.31/1.29 % lits 189
% 3.31/1.29 % lits eq 37
% 3.31/1.29 % fd_pure 0
% 3.31/1.29 % fd_pseudo 0
% 3.31/1.29 % fd_cond 1
% 3.31/1.29 % fd_pseudo_cond 8
% 3.31/1.29 % AC symbols 0
% 3.31/1.29
% 3.31/1.29 % ------ Schedule dynamic 5 is on
% 3.31/1.29
% 3.31/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.31/1.29
% 3.31/1.29
% 3.31/1.29 % ------
% 3.31/1.29 % Current options:
% 3.31/1.29 % ------
% 3.31/1.29
% 3.31/1.29
% 3.31/1.29 %
% 3.31/1.29
% 3.31/1.29 % ------ Proving...
% 3.31/1.29 %
% 3.31/1.29
% 3.31/1.29 % SZS status Theorem for theBenchmark.p
% 3.31/1.29
% 3.31/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.31/1.29
% 3.31/1.29
%------------------------------------------------------------------------------