%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET959+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 02:49:12 PM UTC 2026
% Result : Theorem 2.27s 1.28s
% Output : CNFRefutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 58 ( 10 unt; 0 def)
% Number of atoms : 163 ( 60 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 175 ( 70 ~; 66 |; 28 &)
% ( 6 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 106 !; 20 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,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(f7,conjecture,
! [X0,X1] :
( ( ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) )
& ! [X2] :
~ ( ! [X3,X4] : X2 != ordered_pair(X3,X4)
& in(X2,X1) )
& ! [X2] :
~ ( ! [X3,X4] : X2 != ordered_pair(X3,X4)
& in(X2,X0) ) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ( ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) )
& ! [X2] :
~ ( ! [X3,X4] : X2 != ordered_pair(X3,X4)
& in(X2,X1) )
& ! [X2] :
~ ( ! [X3,X4] : X2 != ordered_pair(X3,X4)
& in(X2,X0) ) )
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f10,plain,
~ ! [X0,X1] :
( ( ! [X8,X9] :
( in(ordered_pair(X8,X9),X0)
<=> in(ordered_pair(X8,X9),X1) )
& ! [X5] :
~ ( ! [X6,X7] : ordered_pair(X6,X7) != X5
& in(X5,X1) )
& ! [X2] :
~ ( ! [X3,X4] : X2 != ordered_pair(X3,X4)
& in(X2,X0) ) )
=> X0 = X1 ),
inference(rectify,[],[f8]) ).
fof(f12,plain,
? [X0,X1] :
( ! [X8,X9] :
( in(ordered_pair(X8,X9),X0)
<=> in(ordered_pair(X8,X9),X1) )
& ! [X5] :
( ? [X6,X7] : ordered_pair(X6,X7) = X5
| ~ in(X5,X1) )
& ! [X2] :
( ? [X3,X4] : ordered_pair(X3,X4) = X2
| ~ in(X2,X0) )
& X0 != X1 ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
? [X0,X1] :
( ! [X8,X9] :
( in(ordered_pair(X8,X9),X0)
<=> in(ordered_pair(X8,X9),X1) )
& ! [X5] :
( ? [X6,X7] : ordered_pair(X6,X7) = X5
| ~ in(X5,X1) )
& ! [X2] :
( ? [X3,X4] : ordered_pair(X3,X4) = X2
| ~ in(X2,X0) )
& X0 != X1 ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f17,plain,
? [X0,X1] :
( ! [X8,X9] :
( ( ~ in(ordered_pair(X8,X9),X0)
| in(ordered_pair(X8,X9),X1) )
& ( ~ in(ordered_pair(X8,X9),X1)
| in(ordered_pair(X8,X9),X0) ) )
& ! [X5] :
( ? [X6,X7] : ordered_pair(X6,X7) = X5
| ~ in(X5,X1) )
& ! [X2] :
( ? [X3,X4] : ordered_pair(X3,X4) = X2
| ~ in(X2,X0) )
& X0 != X1 ),
inference(nnf_transformation,[],[f13]) ).
fof(f18,plain,
( ! [X8,X9] :
( ( ~ in(ordered_pair(X8,X9),sK2)
| in(ordered_pair(X8,X9),sK3) )
& ( ~ in(ordered_pair(X8,X9),sK3)
| in(ordered_pair(X8,X9),sK2) ) )
& ! [X5] :
( ordered_pair(sK6(X5),sK7(X5)) = X5
| ~ in(X5,sK3) )
& ! [X2] :
( ordered_pair(sK4(X2),sK5(X2)) = X2
| ~ in(X2,sK2) )
& sK2 != sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X3,sK4(X2)),skolemize(X4,sK5(X2)),skolemize(X6,sK6(X5)),skolemize(X7,sK7(X5))],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f14]) ).
fof(f20,plain,
! [X0,X1] :
( ( ( in(sK8(X0,X1),X0)
| in(sK8(X0,X1),X1) )
& ( ~ in(sK8(X0,X1),X0)
| ~ in(sK8(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f19]) ).
fof(f22,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f23,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f3]) ).
fof(f27,plain,
! [X8,X9] :
( ~ in(ordered_pair(X8,X9),sK2)
| in(ordered_pair(X8,X9),sK3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X8,X9] :
( ~ in(ordered_pair(X8,X9),sK3)
| in(ordered_pair(X8,X9),sK2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X5] :
( ordered_pair(sK6(X5),sK7(X5)) = X5
| ~ in(X5,sK3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X2] :
( ordered_pair(sK4(X2),sK5(X2)) = X2
| ~ in(X2,sK2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X0,X1] :
( in(sK8(X0,X1),X0)
| in(sK8(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1] :
( ~ in(sK8(X0,X1),X0)
| ~ in(sK8(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X2] :
( unordered_pair(unordered_pair(sK4(X2),sK5(X2)),singleton(sK4(X2))) = X2
| ~ in(X2,sK2) ),
inference(definition_unfolding,[],[f30,f23]) ).
fof(f36,plain,
! [X5] :
( unordered_pair(unordered_pair(sK6(X5),sK7(X5)),singleton(sK6(X5))) = X5
| ~ in(X5,sK3) ),
inference(definition_unfolding,[],[f29,f23]) ).
fof(f37,plain,
! [X8,X9] :
( ~ in(unordered_pair(unordered_pair(X8,X9),singleton(X8)),sK3)
| in(unordered_pair(unordered_pair(X8,X9),singleton(X8)),sK2) ),
inference(definition_unfolding,[],[f28,f23,f23]) ).
fof(f38,plain,
! [X8,X9] :
( ~ in(unordered_pair(unordered_pair(X8,X9),singleton(X8)),sK2)
| in(unordered_pair(unordered_pair(X8,X9),singleton(X8)),sK3) ),
inference(definition_unfolding,[],[f27,f23,f23]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f22]) ).
tcf(c_54,negated_conjecture,
sK2 != sK3,
inference(cnf_transformation,[],[f31]) ).
tcf(c_55,negated_conjecture,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK4(X0),sK5(X0)),singleton(sK4(X0))) = X0 )
| ~ in(X0,sK2) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_56,negated_conjecture,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK6(X0),sK7(X0)),singleton(sK6(X0))) = X0 )
| ~ in(X0,sK3) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_57,negated_conjecture,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK3) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_58,negated_conjecture,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK2) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK8(X0,X1),X1)
| ~ in(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( in(sK8(X0,X1),X1)
| in(sK8(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK3)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK2) ),
inference(prop_impl_just,[status(thm)],[c_57]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK3) ),
inference(renaming,[status(thm)],[c_69]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK2) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_77,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK4(X0),sK5(X0)),singleton(sK4(X0))) = X0 )
| ~ in(X0,sK2) ),
inference(prop_impl_just,[status(thm)],[c_55]) ).
tcf(c_79,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK6(X0),sK7(X0)),singleton(sK6(X0))) = X0 )
| ~ in(X0,sK3) ),
inference(prop_impl_just,[status(thm)],[c_56]) ).
tcf(c_164,plain,
! [X0: $i] :
( ( unordered_pair(singleton(sK6(X0)),unordered_pair(sK6(X0),sK7(X0))) = X0 )
| ~ in(X0,sK3) ),
inference(demodulation,[status(thm)],[c_79,c_50]) ).
tcf(c_171,plain,
! [X0: $i] :
( ( unordered_pair(singleton(sK4(X0)),unordered_pair(sK4(X0),sK5(X0))) = X0 )
| ~ in(X0,sK2) ),
inference(demodulation,[status(thm)],[c_77,c_50]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK2) ),
inference(demodulation,[status(thm)],[c_71,c_50]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK3) ),
inference(demodulation,[status(thm)],[c_70,c_50]) ).
tcf(c_214,negated_conjecture,
sK2 != sK3,
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_508,plain,
! [X0: $i] :
( in(sK8(X0,sK3),X0)
| ( X0 = sK3 )
| ( unordered_pair(singleton(sK6(sK8(X0,sK3))),unordered_pair(sK6(sK8(X0,sK3)),sK7(sK8(X0,sK3)))) = sK8(X0,sK3) ) ),
inference(superposition,[status(thm)],[c_60,c_164]) ).
tcf(c_585,plain,
( ( sK2 = sK3 )
| ( unordered_pair(singleton(sK6(sK8(sK2,sK3))),unordered_pair(sK6(sK8(sK2,sK3)),sK7(sK8(sK2,sK3)))) = sK8(sK2,sK3) )
| ( unordered_pair(singleton(sK4(sK8(sK2,sK3))),unordered_pair(sK4(sK8(sK2,sK3)),sK5(sK8(sK2,sK3)))) = sK8(sK2,sK3) ) ),
inference(superposition,[status(thm)],[c_508,c_171]) ).
tcf(c_591,plain,
( ( unordered_pair(singleton(sK6(sK8(sK2,sK3))),unordered_pair(sK6(sK8(sK2,sK3)),sK7(sK8(sK2,sK3)))) = sK8(sK2,sK3) )
| ( unordered_pair(singleton(sK4(sK8(sK2,sK3))),unordered_pair(sK4(sK8(sK2,sK3)),sK5(sK8(sK2,sK3)))) = sK8(sK2,sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_585,c_214]) ).
tcf(c_605,plain,
( in(unordered_pair(singleton(sK6(sK8(sK2,sK3))),unordered_pair(sK6(sK8(sK2,sK3)),sK7(sK8(sK2,sK3)))),sK2)
| ( unordered_pair(singleton(sK4(sK8(sK2,sK3))),unordered_pair(sK4(sK8(sK2,sK3)),sK5(sK8(sK2,sK3)))) = sK8(sK2,sK3) )
| ~ in(sK8(sK2,sK3),sK3) ),
inference(superposition,[status(thm)],[c_591,c_185]) ).
tcf(c_634,plain,
( ( sK2 = sK3 )
| ~ in(sK8(sK2,sK3),sK3)
| ~ in(sK8(sK2,sK3),sK2) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_659,plain,
( in(sK8(sK2,sK3),sK2)
| ( unordered_pair(singleton(sK4(sK8(sK2,sK3))),unordered_pair(sK4(sK8(sK2,sK3)),sK5(sK8(sK2,sK3)))) = sK8(sK2,sK3) )
| ~ in(sK8(sK2,sK3),sK3) ),
inference(superposition,[status(thm)],[c_591,c_605]) ).
tcf(c_675,plain,
( in(sK8(sK2,sK3),sK3)
| in(sK8(sK2,sK3),sK2)
| ( sK2 = sK3 ) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_678,plain,
( in(sK8(sK2,sK3),sK2)
| ( unordered_pair(singleton(sK4(sK8(sK2,sK3))),unordered_pair(sK4(sK8(sK2,sK3)),sK5(sK8(sK2,sK3)))) = sK8(sK2,sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_659,c_54,c_659,c_675]) ).
tcf(c_682,plain,
unordered_pair(singleton(sK4(sK8(sK2,sK3))),unordered_pair(sK4(sK8(sK2,sK3)),sK5(sK8(sK2,sK3)))) = sK8(sK2,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_678,c_171]) ).
tcf(c_693,plain,
( in(unordered_pair(singleton(sK4(sK8(sK2,sK3))),unordered_pair(sK4(sK8(sK2,sK3)),sK5(sK8(sK2,sK3)))),sK2)
| ~ in(sK8(sK2,sK3),sK3) ),
inference(superposition,[status(thm)],[c_682,c_185]) ).
tcf(c_694,plain,
( in(unordered_pair(singleton(sK4(sK8(sK2,sK3))),unordered_pair(sK4(sK8(sK2,sK3)),sK5(sK8(sK2,sK3)))),sK3)
| ~ in(sK8(sK2,sK3),sK2) ),
inference(superposition,[status(thm)],[c_682,c_178]) ).
tcf(c_696,plain,
( in(sK8(sK2,sK3),sK3)
| ~ in(sK8(sK2,sK3),sK2) ),
inference(light_normalisation,[status(thm)],[c_694,c_682]) ).
tcf(c_699,plain,
( in(sK8(sK2,sK3),sK2)
| ~ in(sK8(sK2,sK3),sK3) ),
inference(light_normalisation,[status(thm)],[c_693,c_682]) ).
tcf(c_712,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_696,c_699,c_675,c_634,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET959+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:22:00 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.27/1.28 % SZS status Started for theBenchmark.p
% 2.27/1.28 % SZS status Theorem for theBenchmark.p
% 2.27/1.28
% 2.27/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.27/1.28
% 2.27/1.28 % ------ iProver source info
% 2.27/1.28
% 2.27/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.27/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.27/1.28 % git: non_committed_changes: false
% 2.27/1.28
% 2.27/1.28 % ------ Parsing...
% 2.27/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.27/1.28
% 2.27/1.28 % ------ Preprocessing... sup_sim: 5 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.27/1.28
% 2.27/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.27/1.28
% 2.27/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.27/1.28 % ------ Proving...
% 2.27/1.28 % ------ Problem Properties
% 2.27/1.28
% 2.27/1.28 %
% 2.27/1.28 % clauses 12
% 2.27/1.28 % conjectures 1
% 2.27/1.28 % EPR 4
% 2.27/1.28 % Horn 11
% 2.27/1.28 % unary 5
% 2.27/1.28 % binary 5
% 2.27/1.28 % lits 21
% 2.27/1.28 % lits eq 6
% 2.27/1.28 % fd_pure 0
% 2.27/1.28 % fd_pseudo 0
% 2.27/1.28 % fd_cond 0
% 2.27/1.28 % fd_pseudo_cond 2
% 2.27/1.28 % AC symbols 0
% 2.27/1.28
% 2.27/1.28 % ------ Schedule dynamic 5 is on
% 2.27/1.28
% 2.27/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.27/1.28
% 2.27/1.28
% 2.27/1.28 % ------
% 2.27/1.28 % Current options:
% 2.27/1.28 % ------
% 2.27/1.28
% 2.27/1.28
% 2.27/1.28 %
% 2.27/1.28
% 2.27/1.28 % ------ Proving...
% 2.27/1.28 %
% 2.27/1.28
% 2.27/1.28 % SZS status Theorem for theBenchmark.p
% 2.27/1.28
% 2.27/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.27/1.28
% 2.27/1.28
%------------------------------------------------------------------------------