%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET988+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:49:16 PM UTC 2026
% Result : Theorem 0.89s 1.28s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 60 ( 9 unt; 0 def)
% Number of atoms : 185 ( 56 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 207 ( 82 ~; 78 |; 35 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 151 ( 0 sgn 131 !; 20 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f30,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f31,conjecture,
! [X0] :
( ( ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> X2 = X3 )
& ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
=> ( function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_1) ).
fof(f32,negated_conjecture,
~ ! [X0] :
( ( ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> X2 = X3 )
& ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
=> ( function(X0)
& relation(X0) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,axiom,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_1) ).
fof(f34,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : X1 != ordered_pair(X2,X3)
& in(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f36,plain,
~ ! [X0] :
( ( ! [X4,X5,X6] :
( ( in(ordered_pair(X4,X6),X0)
& in(ordered_pair(X4,X5),X0) )
=> X5 = X6 )
& ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
=> ( function(X0)
& relation(X0) ) ),
inference(rectify,[],[f32]) ).
fof(f54,plain,
? [X0] :
( ! [X4,X5,X6] :
( ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| X5 = X6 )
& ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) )
& ( ~ function(X0)
| ~ relation(X0) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f55,plain,
? [X0] :
( ! [X4,X5,X6] :
( ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| X5 = X6 )
& ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) )
& ( ~ function(X0)
| ~ relation(X0) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X2 = X3 ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f57,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X2 = X3 ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f68,plain,
( ! [X4,X5,X6] :
( ~ in(ordered_pair(X4,X6),sK9)
| ~ in(ordered_pair(X4,X5),sK9)
| X5 = X6 )
& ! [X1] :
( ordered_pair(sK10(X1),sK11(X1)) = X1
| ~ in(X1,sK9) )
& ( ~ function(sK9)
| ~ relation(sK9) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X2,sK10(X1)),skolemize(X3,sK11(X1))],[f55]) ).
fof(f69,plain,
! [X0] :
( ( ~ function(X0)
| ! [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X2 = X3 ) )
& ( ? [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0)
& X2 != X3 )
| function(X0) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f70,plain,
! [X0] :
( ( ~ function(X0)
| ! [X4,X5,X6] :
( ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| X5 = X6 ) )
& ( ? [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0)
& X2 != X3 )
| function(X0) ) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ( ~ function(X0)
| ! [X4,X5,X6] :
( ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| X5 = X6 ) )
& ( ( in(ordered_pair(sK12(X0),sK14(X0)),X0)
& in(ordered_pair(sK12(X0),sK13(X0)),X0)
& sK13(X0) != sK14(X0) )
| function(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0)),skolemize(X3,sK14(X0))],[f70]) ).
fof(f72,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) )
& ( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
| relation(X0) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f73,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) ) )
& ( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
| relation(X0) ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X4] :
( ordered_pair(sK16(X4),sK17(X4)) = X4
| ~ in(X4,X0) ) )
& ( ( ! [X2,X3] : ordered_pair(X2,X3) != sK15(X0)
& in(sK15(X0),X0) )
| relation(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X1,sK15(X0)),skolemize(X5,sK16(X4)),skolemize(X6,sK17(X4))],[f73]) ).
fof(f81,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f111,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f30]) ).
fof(f112,plain,
! [X6,X4,X5] :
( ~ in(ordered_pair(X4,X6),sK9)
| ~ in(ordered_pair(X4,X5),sK9)
| X5 = X6 ),
inference(cnf_transformation,[],[f68]) ).
fof(f113,plain,
! [X1] :
( ordered_pair(sK10(X1),sK11(X1)) = X1
| ~ in(X1,sK9) ),
inference(cnf_transformation,[],[f68]) ).
fof(f114,plain,
( ~ function(sK9)
| ~ relation(sK9) ),
inference(cnf_transformation,[],[f68]) ).
fof(f116,plain,
! [X0] :
( in(ordered_pair(sK12(X0),sK14(X0)),X0)
| function(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f117,plain,
! [X0] :
( in(ordered_pair(sK12(X0),sK13(X0)),X0)
| function(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f118,plain,
! [X0] :
( sK13(X0) != sK14(X0)
| function(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f120,plain,
! [X2,X3,X0] :
( ordered_pair(X2,X3) != sK15(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f121,plain,
! [X0] :
( in(sK15(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f123,plain,
! [X1] :
( unordered_pair(unordered_pair(sK10(X1),sK11(X1)),singleton(sK10(X1))) = X1
| ~ in(X1,sK9) ),
inference(definition_unfolding,[],[f113,f111]) ).
fof(f124,plain,
! [X6,X4,X5] :
( ~ in(unordered_pair(unordered_pair(X4,X6),singleton(X4)),sK9)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),sK9)
| X5 = X6 ),
inference(definition_unfolding,[],[f112,f111,f111]) ).
fof(f125,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK12(X0),sK13(X0)),singleton(sK12(X0))),X0)
| function(X0) ),
inference(definition_unfolding,[],[f117,f111]) ).
fof(f126,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK12(X0),sK14(X0)),singleton(sK12(X0))),X0)
| function(X0) ),
inference(definition_unfolding,[],[f116,f111]) ).
fof(f128,plain,
! [X2,X3,X0] :
( sK15(X0) != unordered_pair(unordered_pair(X2,X3),singleton(X2))
| relation(X0) ),
inference(definition_unfolding,[],[f120,f111]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f81]) ).
tcf(c_85,negated_conjecture,
( ~ function(sK9)
| ~ relation(sK9) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_86,negated_conjecture,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK10(X0),sK11(X0)),singleton(sK10(X0))) = X0 )
| ~ in(X0,sK9) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_87,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),sK9)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK9) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_88,plain,
! [X0: $i] :
( function(X0)
| ( sK13(X0) != sK14(X0) ) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_89,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK12(X0),sK13(X0)),singleton(sK12(X0))),X0) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_90,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK12(X0),sK14(X0)),singleton(sK12(X0))),X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_92,plain,
! [X0: $i] :
( relation(X0)
| in(sK15(X0),X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X2)
| ( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != sK15(X2) ) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_332,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X2)
| ( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK15(X2) ) ),
inference(demodulation,[status(thm)],[c_93,c_55]) ).
tcf(c_339,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(singleton(sK12(X0)),unordered_pair(sK12(X0),sK14(X0))),X0) ),
inference(demodulation,[status(thm)],[c_90,c_55]) ).
tcf(c_346,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(singleton(sK12(X0)),unordered_pair(sK12(X0),sK13(X0))),X0) ),
inference(demodulation,[status(thm)],[c_89,c_55]) ).
tcf(c_353,plain,
! [X0: $i] :
( ( unordered_pair(singleton(sK10(X0)),unordered_pair(sK10(X0),sK11(X0))) = X0 )
| ~ in(X0,sK9) ),
inference(demodulation,[status(thm)],[c_86,c_55]) ).
tcf(c_370,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X2)),sK9)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK9) ),
inference(demodulation,[status(thm)],[c_87,c_55]) ).
tcf(c_1219,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X2)),sK9)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK9) ),
inference(demodulation,[status(thm)],[c_370]) ).
tcf(c_1220,plain,
! [X0: $i] :
( ( unordered_pair(singleton(sK10(X0)),unordered_pair(sK10(X0),sK11(X0))) = X0 )
| ~ in(X0,sK9) ),
inference(demodulation,[status(thm)],[c_353]) ).
tcf(c_1221,negated_conjecture,
( ~ function(sK9)
| ~ relation(sK9) ),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_1655,plain,
! [X0: $i] :
( function(sK9)
| ( sK14(sK9) = X0 )
| ~ in(unordered_pair(singleton(sK12(sK9)),unordered_pair(sK12(sK9),X0)),sK9) ),
inference(superposition,[status(thm)],[c_339,c_1219]) ).
tcf(c_1679,plain,
( relation(sK9)
| ( unordered_pair(singleton(sK10(sK15(sK9))),unordered_pair(sK10(sK15(sK9)),sK11(sK15(sK9)))) = sK15(sK9) ) ),
inference(superposition,[status(thm)],[c_92,c_1220]) ).
tcf(c_1710,plain,
relation(sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_1679,c_332]) ).
tcf(c_1711,plain,
~ function(sK9),
inference(backward_subsumption_resolution,[status(thm)],[c_1221,c_1710]) ).
tcf(c_1712,plain,
! [X0: $i] :
( ( sK14(sK9) = X0 )
| ~ in(unordered_pair(singleton(sK12(sK9)),unordered_pair(sK12(sK9),X0)),sK9) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1655,c_1711]) ).
tcf(c_2108,plain,
( function(sK9)
| ( sK13(sK9) = sK14(sK9) ) ),
inference(superposition,[status(thm)],[c_346,c_1712]) ).
tcf(c_2109,plain,
sK13(sK9) = sK14(sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_2108,c_1711]) ).
tcf(c_2162,plain,
( function(sK9)
| ( sK13(sK9) != sK14(sK9) ) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_2163,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2162,c_2109,c_1711]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET988+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n007.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 : Thu Sep 24 12:29:24 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 0.89/1.28 % SZS status Started for theBenchmark.p
% 0.89/1.28 % SZS status Theorem for theBenchmark.p
% 0.89/1.28
% 0.89/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.89/1.28
% 0.89/1.28 % ------ iProver source info
% 0.89/1.28
% 0.89/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.89/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.89/1.28 % git: non_committed_changes: false
% 0.89/1.28
% 0.89/1.28 % ------ Parsing...
% 0.89/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.89/1.28
% 0.89/1.28 % ------ Preprocessing... sup_sim: 7 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 %
% 0.89/1.28
% 0.89/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.89/1.28
% 0.89/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.89/1.28 % ------ Proving...
% 0.89/1.28 % ------ Problem Properties
% 0.89/1.28
% 0.89/1.28 %
% 0.89/1.28 % clauses 41
% 0.89/1.28 % conjectures 1
% 0.89/1.28 % EPR 20
% 0.89/1.28 % Horn 36
% 0.89/1.28 % unary 19
% 0.89/1.28 % binary 15
% 0.89/1.28 % lits 71
% 0.89/1.28 % lits eq 9
% 0.89/1.28 % fd_pure 0
% 0.89/1.28 % fd_pseudo 0
% 0.89/1.28 % fd_cond 1
% 0.89/1.28 % fd_pseudo_cond 3
% 0.89/1.28 % AC symbols 0
% 0.89/1.28
% 0.89/1.28 % ------ Schedule dynamic 5 is on
% 0.89/1.28
% 0.89/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.89/1.28
% 0.89/1.28
% 0.89/1.28 % ------
% 0.89/1.28 % Current options:
% 0.89/1.28 % ------
% 0.89/1.28
% 0.89/1.28
% 0.89/1.28 %
% 0.89/1.28
% 0.89/1.28 % ------ Proving...
% 0.89/1.28 %
% 0.89/1.28
% 0.89/1.28 % SZS status Theorem for theBenchmark.p
% 0.89/1.28
% 0.89/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.89/1.28
% 0.89/1.28
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