%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG114+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 02:39:12 PM UTC 2026
% Result : Theorem 10.75s 7.31s
% Output : CNFRefutation 10.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 12 unt; 0 def)
% Number of atoms : 243 ( 69 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 296 ( 92 ~; 74 |; 113 &)
% ( 9 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 75 !; 36 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( sdtasdt0(xb,X1) = X0
& aElement0(X1) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
& 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/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f45,axiom,
( ! [X0] :
( ( X0 != sz00
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
fof(f47,conjecture,
? [X0,X1] :
( xu = sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1))
& aElement0(X1)
& aElement0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f48,negated_conjecture,
~ ? [X0,X1] :
( xu = sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1))
& aElement0(X1)
& aElement0(X0) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f50,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X7] :
( aElementOf0(X7,xI)
<=> ? [X8,X9] :
( sdtpldt0(X8,X9) = X7
& aElementOf0(X9,slsdtgt0(xb))
& aElementOf0(X8,slsdtgt0(xa)) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xb))
<=> ? [X6] :
( sdtasdt0(xb,X6) = X5
& aElement0(X6) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xa))
<=> ? [X4] :
( sdtasdt0(xa,X4) = X3
& aElement0(X4) ) )
& 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,[],[f42]) ).
fof(f53,plain,
( ! [X2] :
( ( sz00 != X2
& ( aElementOf0(X2,xI)
| ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(rectify,[],[f45]) ).
fof(f64,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X7] :
( aElementOf0(X7,xI)
<=> ? [X8,X9] :
( sdtpldt0(X8,X9) = X7
& aElementOf0(X9,slsdtgt0(xb))
& aElementOf0(X8,slsdtgt0(xa)) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xb))
<=> ? [X6] :
( sdtasdt0(xb,X6) = X5
& aElement0(X6) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xa))
<=> ? [X4] :
( sdtasdt0(xa,X4) = X3
& aElement0(X4) ) )
& 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,[],[f50]) ).
fof(f65,plain,
( ! [X2] :
( sz00 = X2
| ( ~ aElementOf0(X2,xI)
& ! [X3,X4] :
( sdtpldt0(X3,X4) != X2
| ~ aElementOf0(X4,slsdtgt0(xb))
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f66,plain,
( ! [X2] :
( sz00 = X2
| ( ~ aElementOf0(X2,xI)
& ! [X3,X4] :
( sdtpldt0(X3,X4) != X2
| ~ aElementOf0(X4,slsdtgt0(xb))
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(flattening,[],[f65]) ).
fof(f68,plain,
! [X0,X1] :
( xu != sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f118,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X7] :
( ( ~ aElementOf0(X7,xI)
| ? [X8,X9] :
( sdtpldt0(X8,X9) = X7
& aElementOf0(X9,slsdtgt0(xb))
& aElementOf0(X8,slsdtgt0(xa)) ) )
& ( ! [X8,X9] :
( sdtpldt0(X8,X9) != X7
| ~ aElementOf0(X9,slsdtgt0(xb))
| ~ aElementOf0(X8,slsdtgt0(xa)) )
| aElementOf0(X7,xI) ) )
& ! [X5] :
( ( ~ aElementOf0(X5,slsdtgt0(xb))
| ? [X6] :
( sdtasdt0(xb,X6) = X5
& aElement0(X6) ) )
& ( ! [X6] :
( sdtasdt0(xb,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ? [X4] :
( sdtasdt0(xa,X4) = X3
& aElement0(X4) ) )
& ( ! [X4] :
( sdtasdt0(xa,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xa)) ) )
& 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(nnf_transformation,[],[f64]) ).
fof(f119,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X9] :
( ( ~ aElementOf0(X9,xI)
| ? [X12,X13] :
( sdtpldt0(X12,X13) = X9
& aElementOf0(X13,slsdtgt0(xb))
& aElementOf0(X12,slsdtgt0(xa)) ) )
& ( ! [X10,X11] :
( sdtpldt0(X10,X11) != X9
| ~ aElementOf0(X11,slsdtgt0(xb))
| ~ aElementOf0(X10,slsdtgt0(xa)) )
| aElementOf0(X9,xI) ) )
& ! [X6] :
( ( ~ aElementOf0(X6,slsdtgt0(xb))
| ? [X8] :
( sdtasdt0(xb,X8) = X6
& aElement0(X8) ) )
& ( ! [X7] :
( sdtasdt0(xb,X7) != X6
| ~ aElement0(X7) )
| aElementOf0(X6,slsdtgt0(xb)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ? [X5] :
( sdtasdt0(xa,X5) = X3
& aElement0(X5) ) )
& ( ! [X4] :
( sdtasdt0(xa,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xa)) ) )
& 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,[],[f118]) ).
fof(f120,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X9] :
( ( ~ aElementOf0(X9,xI)
| ( sdtpldt0(sK10(X9),sK11(X9)) = X9
& aElementOf0(sK11(X9),slsdtgt0(xb))
& aElementOf0(sK10(X9),slsdtgt0(xa)) ) )
& ( ! [X10,X11] :
( sdtpldt0(X10,X11) != X9
| ~ aElementOf0(X11,slsdtgt0(xb))
| ~ aElementOf0(X10,slsdtgt0(xa)) )
| aElementOf0(X9,xI) ) )
& ! [X6] :
( ( ~ aElementOf0(X6,slsdtgt0(xb))
| ( sdtasdt0(xb,sK9(X6)) = X6
& aElement0(sK9(X6)) ) )
& ( ! [X7] :
( sdtasdt0(xb,X7) != X6
| ~ aElement0(X7) )
| aElementOf0(X6,slsdtgt0(xb)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ( sdtasdt0(xa,sK8(X3)) = X3
& aElement0(sK8(X3)) ) )
& ( ! [X4] :
( sdtasdt0(xa,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xa)) ) )
& 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(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X5,sK8(X3)),skolemize(X8,sK9(X6)),skolemize(X12,sK10(X9)),skolemize(X13,sK11(X9))],[f119]) ).
fof(f125,plain,
( ! [X2] :
( sz00 = X2
| ( ~ aElementOf0(X2,xI)
& ! [X3,X4] :
( sdtpldt0(X3,X4) != X2
| ~ aElementOf0(X4,slsdtgt0(xb))
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& xu = sdtpldt0(sK21,sK22)
& aElementOf0(sK22,slsdtgt0(xb))
& aElementOf0(sK21,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22]),skolemize(X0,sK21),skolemize(X1,sK22)],[f66]) ).
fof(f181,plain,
! [X6] :
( ~ aElementOf0(X6,slsdtgt0(xb))
| sdtasdt0(xb,sK9(X6)) = X6 ),
inference(cnf_transformation,[],[f120]) ).
fof(f182,plain,
! [X6] :
( ~ aElementOf0(X6,slsdtgt0(xb))
| aElement0(sK9(X6)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f184,plain,
! [X3] :
( ~ aElementOf0(X3,slsdtgt0(xa))
| sdtasdt0(xa,sK8(X3)) = X3 ),
inference(cnf_transformation,[],[f120]) ).
fof(f185,plain,
! [X3] :
( ~ aElementOf0(X3,slsdtgt0(xa))
| aElement0(sK8(X3)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f218,plain,
xu = sdtpldt0(sK21,sK22),
inference(cnf_transformation,[],[f125]) ).
fof(f219,plain,
aElementOf0(sK22,slsdtgt0(xb)),
inference(cnf_transformation,[],[f125]) ).
fof(f220,plain,
aElementOf0(sK21,slsdtgt0(xa)),
inference(cnf_transformation,[],[f125]) ).
fof(f227,plain,
! [X0,X1] :
( xu != sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_77,plain,
! [X0: $i] :
( aElement0(sK8(X0))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_78,plain,
! [X0: $i] :
( ( sdtasdt0(xa,sK8(X0)) = X0 )
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_80,plain,
! [X0: $i] :
( aElement0(sK9(X0))
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_81,plain,
! [X0: $i] :
( ( sdtasdt0(xb,sK9(X0)) = X0 )
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_110,plain,
aElementOf0(sK21,slsdtgt0(xa)),
inference(cnf_transformation,[],[f220]) ).
tcf(c_111,plain,
aElementOf0(sK22,slsdtgt0(xb)),
inference(cnf_transformation,[],[f219]) ).
tcf(c_112,plain,
sdtpldt0(sK21,sK22) = xu,
inference(cnf_transformation,[],[f218]) ).
tcf(c_123,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ( sdtpldt0(sdtasdt0(xa,X0),sdtasdt0(xb,X1)) != xu ) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_8753,plain,
aElement0(sK8(sK21)),
inference(superposition,[status(thm)],[c_110,c_77]) ).
tcf(c_8761,plain,
aElement0(sK9(sK22)),
inference(superposition,[status(thm)],[c_111,c_80]) ).
tcf(c_9634,plain,
sdtasdt0(xa,sK8(sK21)) = sK21,
inference(superposition,[status(thm)],[c_110,c_78]) ).
tcf(c_9662,plain,
sdtasdt0(xb,sK9(sK22)) = sK22,
inference(superposition,[status(thm)],[c_111,c_81]) ).
tcf(c_19512,plain,
! [X0: $i] :
( ~ aElement0(X0)
| ~ aElement0(sK8(sK21))
| ( sdtpldt0(sK21,sdtasdt0(xb,X0)) != xu ) ),
inference(superposition,[status(thm)],[c_9634,c_123]) ).
tcf(c_19524,plain,
! [X0: $i] :
( ~ aElement0(X0)
| ( sdtpldt0(sK21,sdtasdt0(xb,X0)) != xu ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19512,c_8753]) ).
tcf(c_19800,plain,
( ~ aElement0(sK9(sK22))
| ( sdtpldt0(sK21,sK22) != xu ) ),
inference(superposition,[status(thm)],[c_9662,c_19524]) ).
tcf(c_19812,plain,
~ aElement0(sK9(sK22)),
inference(ground_joinability,[status(thm)],[c_19800,c_112]) ).
tcf(c_19813,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_19812,c_8761]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG114+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n003.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 08:20:14 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 10.75/7.31 % SZS status Started for theBenchmark.p
% 10.75/7.31 % SZS status Theorem for theBenchmark.p
% 10.75/7.31
% 10.75/7.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.75/7.31
% 10.75/7.31 % ------ iProver source info
% 10.75/7.31
% 10.75/7.31 % git: date: 2026-07-19 20:42:38 +0200
% 10.75/7.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.75/7.31 % git: non_committed_changes: false
% 10.75/7.31
% 10.75/7.31 % ------ Parsing...
% 10.75/7.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.75/7.31
% 10.75/7.31 % ------ 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 %
% 10.75/7.31
% 10.75/7.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.75/7.31
% 10.75/7.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.75/7.31 % ------ Proving...
% 10.75/7.31 % ------ Problem Properties
% 10.75/7.31
% 10.75/7.31 %
% 10.75/7.31 % clauses 135
% 10.75/7.31 % conjectures 1
% 10.75/7.31 % EPR 40
% 10.75/7.31 % Horn 113
% 10.75/7.31 % unary 38
% 10.75/7.31 % binary 29
% 10.75/7.31 % lits 359
% 10.75/7.31 % lits eq 60
% 10.75/7.31 % fd_pure 0
% 10.75/7.31 % fd_pseudo 0
% 10.75/7.31 % fd_cond 5
% 10.75/7.31 % fd_pseudo_cond 8
% 10.75/7.31 % AC symbols 0
% 10.75/7.31
% 10.75/7.31 % ------ Schedule dynamic 5 is on
% 10.75/7.31
% 10.75/7.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.75/7.31
% 10.75/7.31
% 10.75/7.31 % ------
% 10.75/7.31 % Current options:
% 10.75/7.31 % ------
% 10.75/7.31
% 10.75/7.31
% 10.75/7.31 %
% 10.75/7.31
% 10.75/7.31 % ------ Proving...
% 10.75/7.31 %
% 10.75/7.31
% 10.75/7.31 % SZS status Theorem for theBenchmark.p
% 10.75/7.31
% 10.75/7.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.75/7.31
% 10.75/7.31
%------------------------------------------------------------------------------