%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG109+4 : 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 : n003.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 02:39:11 PM UTC 2026
% Result : Theorem 0.61s 1.59s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 21 unt; 0 def)
% Number of atoms : 201 ( 79 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 218 ( 65 ~; 54 |; 82 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 53 !; 31 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] :
( aElement0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(f39,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(f40,axiom,
( xb != sz00
| xa != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).
fof(f43,axiom,
( aElementOf0(xb,slsdtgt0(xb))
& ? [X0] :
( sdtasdt0(xb,X0) = xb
& aElement0(X0) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [X0] :
( sdtasdt0(xb,X0) = sz00
& aElement0(X0) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [X0] :
( sdtasdt0(xa,X0) = xa
& aElement0(X0) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [X0] :
( sdtasdt0(xa,X0) = sz00
& aElement0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
fof(f44,conjecture,
? [X0] :
( X0 != sz00
& ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( sdtasdt0(xa,X2) = X1
& aElement0(X2) ) )
=> ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( sdtasdt0(xb,X2) = X1
& aElement0(X2) ) )
=> ( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ? [X0] :
( X0 != sz00
& ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( sdtasdt0(xa,X2) = X1
& aElement0(X2) ) )
=> ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( sdtasdt0(xb,X2) = X1
& aElement0(X2) ) )
=> ( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f48,plain,
( aElementOf0(xb,slsdtgt0(xb))
& ? [X3] :
( xb = sdtasdt0(xb,X3)
& aElement0(X3) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [X2] :
( sz00 = sdtasdt0(xb,X2)
& aElement0(X2) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [X1] :
( xa = sdtasdt0(xa,X1)
& aElement0(X1) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [X0] :
( sdtasdt0(xa,X0) = sz00
& aElement0(X0) ) ),
inference(rectify,[],[f43]) ).
fof(f49,plain,
~ ? [X0] :
( X0 != sz00
& ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( sdtasdt0(xa,X2) = X1
& aElement0(X2) ) )
=> ( ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
=> ( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [X5,X6] :
( sdtpldt0(X5,X6) = X0
& aElementOf0(X6,slsdtgt0(xb))
& aElementOf0(X5,slsdtgt0(xa)) ) ) ) ) ),
inference(rectify,[],[f45]) ).
fof(f57,plain,
! [X0] :
( sz00 = X0
| ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( sdtasdt0(xa,X2) = X1
& aElement0(X2) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X0
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) ),
inference(ennf_transformation,[],[f49]) ).
fof(f58,plain,
! [X0] :
( sz00 = X0
| ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( sdtasdt0(xa,X2) = X1
& aElement0(X2) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X0
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) ),
inference(flattening,[],[f57]) ).
fof(f66,plain,
! [X0] :
( ~ aElement0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f107,plain,
( aElementOf0(xb,slsdtgt0(xb))
& xb = sdtasdt0(xb,sK14)
& aElement0(sK14)
& aElementOf0(sz00,slsdtgt0(xb))
& sz00 = sdtasdt0(xb,sK13)
& aElement0(sK13)
& aElementOf0(xa,slsdtgt0(xa))
& xa = sdtasdt0(xa,sK12)
& aElement0(sK12)
& aElementOf0(sz00,slsdtgt0(xa))
& sz00 = sdtasdt0(xa,sK11)
& aElement0(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X3,sK14)],[f48]) ).
fof(f108,plain,
! [X0] :
( sz00 = X0
| ( ! [X1] :
( ( ~ aElementOf0(X1,slsdtgt0(xa))
| ? [X2] :
( sdtasdt0(xa,X2) = X1
& aElement0(X2) ) )
& ( ! [X2] :
( sdtasdt0(xa,X2) != X1
| ~ aElement0(X2) )
| aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xb))
| ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ( ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xb)) ) )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X0
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f109,plain,
! [X0] :
( sz00 = X0
| ( ! [X6] :
( ( ~ aElementOf0(X6,slsdtgt0(xa))
| ? [X8] :
( sdtasdt0(xa,X8) = X6
& aElement0(X8) ) )
& ( ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) )
| aElementOf0(X6,slsdtgt0(xa)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xb))
| ? [X5] :
( sdtasdt0(xb,X5) = X3
& aElement0(X5) ) )
& ( ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xb)) ) )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f108]) ).
fof(f110,plain,
! [X0] :
( sz00 = X0
| ( ! [X6] :
( ( ~ aElementOf0(X6,slsdtgt0(xa))
| ( sdtasdt0(xa,sK16(X6)) = X6
& aElement0(sK16(X6)) ) )
& ( ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) )
| aElementOf0(X6,slsdtgt0(xa)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xb))
| ( sdtasdt0(xb,sK15(X3)) = X3
& aElement0(sK15(X3)) ) )
& ( ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xb)) ) )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X5,sK15(X3)),skolemize(X8,sK16(X6))],[f109]) ).
fof(f135,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f136,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f137,plain,
( sz00 != xb
| sz00 != xa ),
inference(cnf_transformation,[],[f40]) ).
fof(f173,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[],[f107]) ).
fof(f176,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(cnf_transformation,[],[f107]) ).
fof(f179,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnf_transformation,[],[f107]) ).
fof(f182,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[],[f107]) ).
fof(f192,plain,
! [X2,X0,X1] :
( sz00 = X0
| sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f198,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f66]) ).
fof(f199,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f66]) ).
fof(f256,plain,
! [X2,X1] :
( sz00 = sdtpldt0(X1,X2)
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(equality_resolution,[],[f192]) ).
tcf(c_49,plain,
aElement0(xa),
inference(cnf_transformation,[],[f136]) ).
tcf(c_50,plain,
aElement0(xb),
inference(cnf_transformation,[],[f135]) ).
tcf(c_51,plain,
( ( xb != sz00 )
| ( xa != sz00 ) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_89,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[],[f182]) ).
tcf(c_92,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnf_transformation,[],[f179]) ).
tcf(c_95,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(cnf_transformation,[],[f176]) ).
tcf(c_98,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[],[f173]) ).
tcf(c_99,negated_conjecture,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sz00 )
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f256]) ).
tcf(c_112,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = X0 )
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_113,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_7574,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = sz00 )
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(superposition,[status(thm)],[c_89,c_99]) ).
tcf(c_7584,plain,
! [X0: $i] :
( ( sdtpldt0(xa,X0) = sz00 )
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(superposition,[status(thm)],[c_92,c_99]) ).
tcf(c_7769,plain,
sdtpldt0(sz00,xb) = sz00,
inference(superposition,[status(thm)],[c_98,c_7574]) ).
tcf(c_7774,plain,
sdtpldt0(xa,sz00) = sz00,
inference(superposition,[status(thm)],[c_95,c_7584]) ).
tcf(c_9300,plain,
sdtpldt0(xa,sz00) = xa,
inference(superposition,[status(thm)],[c_49,c_112]) ).
tcf(c_9350,plain,
xa = sz00,
inference(demodulation,[status(thm)],[c_7774,c_9300]) ).
tcf(c_9351,plain,
xb != sz00,
inference(backward_subsumption_resolution,[status(thm)],[c_51,c_9350]) ).
tcf(c_9372,plain,
sdtpldt0(xa,xb) = xa,
inference(demodulation,[status(thm)],[c_7769,c_9350]) ).
tcf(c_9438,plain,
! [X0: $i] :
( ( sdtpldt0(xa,X0) = X0 )
| ~ aElement0(X0) ),
inference(light_normalisation,[status(thm)],[c_113,c_9350]) ).
tcf(c_9446,plain,
sdtpldt0(xa,xb) = xb,
inference(superposition,[status(thm)],[c_50,c_9438]) ).
tcf(c_9465,plain,
xa = xb,
inference(light_normalisation,[status(thm)],[c_9446,c_9372]) ).
tcf(c_9721,plain,
$false,
inference(ground_joinability,[status(thm)],[c_9351,c_9350,c_9465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG109+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.61 % Computer : n003.cluster.edu
% 0.13/0.61 % Model : x86_64 x86_64
% 0.13/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.61 % Memory : 8046.5625MB
% 0.13/0.61 % OS : Linux 6.8.0-71-generic
% 0.13/0.61 % CPULimit : 300
% 0.13/0.61 % WCLimit : 300
% 0.13/0.61 % DateTime : Thu Sep 24 08:18:37 UTC 2026
% 0.13/0.61 % CPUTime :
% 0.13/0.61 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.67 Running first-order theorem proving
% 0.18/0.67 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
% 0.18/0.69
% 0.18/0.69 % ======== iProver multi-core TPTP/SMT =========
% 0.18/0.69
% 0.18/0.69 % Detected problem language: tptp
% 0.18/0.71 % Proving...
% 0.61/1.59 % SZS status Started for theBenchmark.p
% 0.61/1.59 % SZS status Theorem for theBenchmark.p
% 0.61/1.59
% 0.61/1.59 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.61/1.59
% 0.61/1.59 % ------ iProver source info
% 0.61/1.59
% 0.61/1.59 % git: date: 2026-07-19 20:42:38 +0200
% 0.61/1.59 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.61/1.59 % git: non_committed_changes: false
% 0.61/1.59
% 0.61/1.59 % ------ Parsing...
% 0.61/1.59 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.61/1.59
% 0.61/1.59 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.61/1.59
% 0.61/1.59 % ------ Preprocessing... gs_s sp: 8 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.61/1.59
% 0.61/1.59 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.61/1.59 % ------ Proving...
% 0.61/1.59 % ------ Problem Properties
% 0.61/1.59
% 0.61/1.59 %
% 0.61/1.59 % clauses 119
% 0.61/1.59 % conjectures 10
% 0.61/1.59 % EPR 38
% 0.61/1.59 % Horn 97
% 0.61/1.59 % unary 28
% 0.61/1.59 % binary 27
% 0.61/1.59 % lits 327
% 0.61/1.59 % lits eq 48
% 0.61/1.59 % fd_pure 0
% 0.61/1.59 % fd_pseudo 0
% 0.61/1.59 % fd_cond 3
% 0.61/1.59 % fd_pseudo_cond 8
% 0.61/1.59 % AC symbols 0
% 0.61/1.59
% 0.61/1.59 % ------ Schedule dynamic 5 is on
% 0.61/1.59
% 0.61/1.59 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.61/1.59
% 0.61/1.59
% 0.61/1.59 % ------
% 0.61/1.59 % Current options:
% 0.61/1.59 % ------
% 0.61/1.59
% 0.61/1.59
% 0.61/1.59 %
% 0.61/1.59
% 0.61/1.59 % ------ Proving...
% 0.61/1.59 %
% 0.61/1.59
% 0.61/1.59 % SZS status Theorem for theBenchmark.p
% 0.61/1.59
% 0.61/1.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.61/1.59
%------------------------------------------------------------------------------