%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET022-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 02:46:07 PM UTC 2026
% Result : Unsatisfiable 60.95s 9.13s
% Output : CNFRefutation 60.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 10 unt; 0 def)
% Number of atoms : 100 ( 44 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 104 ( 51 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 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 : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',a2) ).
fof(f9,axiom,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',singleton_set) ).
fof(f10,axiom,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(singleton_set(X0),non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
fof(f17,axiom,
! [X0,X1] :
( little_set(f4(X0,X1))
| ~ member(X0,first(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',first1) ).
fof(f18,axiom,
! [X0,X1] :
( little_set(f5(X0,X1))
| ~ member(X0,first(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',first2) ).
fof(f19,axiom,
! [X0,X1] :
( X1 = ordered_pair(f4(X0,X1),f5(X0,X1))
| ~ member(X0,first(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',first3) ).
fof(f20,plain,
! [X0,X1] :
( ordered_pair(f4(X0,X1),f5(X0,X1)) = X1
| ~ member(X0,first(X1)) ),
inference(reorient_equations,[],[f19]) ).
fof(f73,axiom,
member(empty_set,infinity),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',infinity2) ).
fof(f110,axiom,
! [X0] :
( member(f24(X0),X0)
| X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',regularity1) ).
fof(f111,plain,
! [X0] :
( member(f24(X0),X0)
| empty_set = X0 ),
inference(reorient_equations,[],[f110]) ).
fof(f167,axiom,
! [X0,X1] :
( first(ordered_pair(X0,X1)) = X0
| ~ little_set(X1)
| ~ little_set(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_first) ).
fof(f170,negated_conjecture,
~ little_set(first(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_first_component_is_small) ).
fof(f172,plain,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),
inference(definition_unfolding,[],[f10,f9]) ).
fof(f176,plain,
! [X0,X1] :
( non_ordered_pair(non_ordered_pair(f4(X0,X1),f4(X0,X1)),non_ordered_pair(f4(X0,X1),f5(X0,X1))) = X1
| ~ member(X0,first(X1)) ),
inference(definition_unfolding,[],[f20,f172]) ).
fof(f201,plain,
! [X0,X1] :
( first(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1))) = X0
| ~ little_set(X1)
| ~ little_set(X0) ),
inference(definition_unfolding,[],[f167,f172]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i] :
( little_set(X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( little_set(f4(X0,X1))
| ~ member(X0,first(X1)) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] :
( little_set(f5(X0,X1))
| ~ member(X0,first(X1)) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] :
( ( non_ordered_pair(non_ordered_pair(f4(X0,X1),f4(X0,X1)),non_ordered_pair(f4(X0,X1),f5(X0,X1))) = X1 )
| ~ member(X0,first(X1)) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_254,plain,
member(empty_set,infinity),
inference(cnf_transformation,[],[f73]) ).
tcf(c_291,plain,
! [X0: $i] :
( member(f24(X0),X0)
| ( X0 = empty_set ) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i] :
( ( first(non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1))) = X0 )
| ~ little_set(X1)
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_340,negated_conjecture,
~ little_set(first(a)),
inference(cnf_transformation,[],[f170]) ).
tcf(c_9541,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_9543,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9544,plain,
! [X0: $i,X1: $i] :
( little_set(X0)
| ~ little_set(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9547,plain,
! [X0: $i,X1: $i] :
( ( first(X0) = first(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_11122,plain,
( little_set(empty_set)
| ~ member(empty_set,infinity) ),
inference(instantiation,[status(thm)],[c_198]) ).
tcf(c_13371,plain,
! [X0: $i] :
( little_set(first(a))
| ~ little_set(X0)
| ( first(a) != X0 ) ),
inference(instantiation,[status(thm)],[c_9544]) ).
tcf(c_13372,plain,
( little_set(first(a))
| ~ little_set(empty_set)
| ( first(a) != empty_set ) ),
inference(instantiation,[status(thm)],[c_13371]) ).
tcf(c_13373,plain,
! [X0: $i,X1: $i] :
( little_set(first(X0))
| ~ little_set(X1)
| ( first(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_9544]) ).
tcf(c_15947,plain,
( member(f24(first(a)),first(a))
| ( first(a) = empty_set ) ),
inference(instantiation,[status(thm)],[c_291]) ).
tcf(c_15952,plain,
! [X0: $i] :
( little_set(first(a))
| ~ little_set(first(X0))
| ( first(a) != first(X0) ) ),
inference(instantiation,[status(thm)],[c_13371]) ).
tcf(c_15953,plain,
! [X0: $i] :
( ( first(a) = first(X0) )
| ( a != X0 ) ),
inference(instantiation,[status(thm)],[c_9547]) ).
tcf(c_16234,plain,
! [X0: $i,X1: $i] :
( ( a = X0 )
| ( a != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_9543]) ).
tcf(c_22678,plain,
( ( non_ordered_pair(non_ordered_pair(f4(f24(first(a)),a),f4(f24(first(a)),a)),non_ordered_pair(f4(f24(first(a)),a),f5(f24(first(a)),a))) = a )
| ~ member(f24(first(a)),first(a)) ),
inference(instantiation,[status(thm)],[c_212]) ).
tcf(c_22680,plain,
( little_set(f5(f24(first(a)),a))
| ~ member(f24(first(a)),first(a)) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_22681,plain,
( little_set(f4(f24(first(a)),a))
| ~ member(f24(first(a)),first(a)) ),
inference(instantiation,[status(thm)],[c_210]) ).
tcf(c_22743,plain,
a = a,
inference(instantiation,[status(thm)],[c_9541]) ).
tcf(c_28061,plain,
! [X0: $i] :
( ( a = X0 )
| ( a != a )
| ( X0 != a ) ),
inference(instantiation,[status(thm)],[c_16234]) ).
tcf(c_41662,plain,
( ( a = non_ordered_pair(non_ordered_pair(f4(f24(first(a)),a),f4(f24(first(a)),a)),non_ordered_pair(f4(f24(first(a)),a),f5(f24(first(a)),a))) )
| ( a != a )
| ( non_ordered_pair(non_ordered_pair(f4(f24(first(a)),a),f4(f24(first(a)),a)),non_ordered_pair(f4(f24(first(a)),a),f5(f24(first(a)),a))) != a ) ),
inference(instantiation,[status(thm)],[c_28061]) ).
tcf(c_48409,plain,
( ( first(a) = first(non_ordered_pair(non_ordered_pair(f4(f24(first(a)),a),f4(f24(first(a)),a)),non_ordered_pair(f4(f24(first(a)),a),f5(f24(first(a)),a)))) )
| ( a != non_ordered_pair(non_ordered_pair(f4(f24(first(a)),a),f4(f24(first(a)),a)),non_ordered_pair(f4(f24(first(a)),a),f5(f24(first(a)),a))) ) ),
inference(instantiation,[status(thm)],[c_15953]) ).
tcf(c_67562,plain,
( little_set(first(a))
| ~ little_set(first(non_ordered_pair(non_ordered_pair(f4(f24(first(a)),a),f4(f24(first(a)),a)),non_ordered_pair(f4(f24(first(a)),a),f5(f24(first(a)),a)))))
| ( first(a) != first(non_ordered_pair(non_ordered_pair(f4(f24(first(a)),a),f4(f24(first(a)),a)),non_ordered_pair(f4(f24(first(a)),a),f5(f24(first(a)),a)))) ) ),
inference(instantiation,[status(thm)],[c_15952]) ).
tcf(c_73680,plain,
! [X0: $i] :
( little_set(first(non_ordered_pair(non_ordered_pair(f4(f24(first(a)),a),f4(f24(first(a)),a)),non_ordered_pair(f4(f24(first(a)),a),f5(f24(first(a)),a)))))
| ~ little_set(X0)
| ( first(non_ordered_pair(non_ordered_pair(f4(f24(first(a)),a),f4(f24(first(a)),a)),non_ordered_pair(f4(f24(first(a)),a),f5(f24(first(a)),a)))) != X0 ) ),
inference(instantiation,[status(thm)],[c_13373]) ).
tcf(c_82210,plain,
( little_set(first(non_ordered_pair(non_ordered_pair(f4(f24(first(a)),a),f4(f24(first(a)),a)),non_ordered_pair(f4(f24(first(a)),a),f5(f24(first(a)),a)))))
| ~ little_set(f4(f24(first(a)),a))
| ( first(non_ordered_pair(non_ordered_pair(f4(f24(first(a)),a),f4(f24(first(a)),a)),non_ordered_pair(f4(f24(first(a)),a),f5(f24(first(a)),a)))) != f4(f24(first(a)),a) ) ),
inference(instantiation,[status(thm)],[c_73680]) ).
tcf(c_82211,plain,
( ( first(non_ordered_pair(non_ordered_pair(f4(f24(first(a)),a),f4(f24(first(a)),a)),non_ordered_pair(f4(f24(first(a)),a),f5(f24(first(a)),a)))) = f4(f24(first(a)),a) )
| ~ little_set(f5(f24(first(a)),a))
| ~ little_set(f4(f24(first(a)),a)) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_82212,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_82211,c_82210,c_67562,c_48409,c_41662,c_22743,c_22678,c_22680,c_22681,c_15947,c_13372,c_11122,c_340,c_254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET022-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 09:14:05 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 60.95/9.13 % SZS status Started for theBenchmark.p
% 60.95/9.13 % SZS status Unsatisfiable for theBenchmark.p
% 60.95/9.13
% 60.95/9.13 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 60.95/9.13
% 60.95/9.13 % ------ iProver source info
% 60.95/9.13
% 60.95/9.13 % git: date: 2026-07-19 20:42:38 +0200
% 60.95/9.13 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 60.95/9.13 % git: non_committed_changes: false
% 60.95/9.13
% 60.95/9.13 % ------ Parsing...% successful
% 60.95/9.13
% 60.95/9.13
% 60.95/9.13 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 60.95/9.13
% 60.95/9.13 % ------ 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: 1 0s sf_e pe_s pe_e %
% 60.95/9.13
% 60.95/9.13 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 60.95/9.13
% 60.95/9.13 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 60.95/9.13 % ------ Proving...
% 60.95/9.13 % ------ Problem Properties
% 60.95/9.13
% 60.95/9.13 %
% 60.95/9.13 % clauses 137
% 60.95/9.13 % conjectures 1
% 60.95/9.13 % EPR 22
% 60.95/9.13 % Horn 118
% 60.95/9.13 % unary 7
% 60.95/9.13 % binary 89
% 60.95/9.13 % lits 344
% 60.95/9.13 % lits eq 35
% 60.95/9.13 % fd_pure 0
% 60.95/9.13 % fd_pseudo 0
% 60.95/9.13 % fd_cond 4
% 60.95/9.13 % fd_pseudo_cond 10
% 60.95/9.13 % AC symbols 0
% 60.95/9.13
% 60.95/9.13 % ------ Input Options Time Limit: Unbounded
% 60.95/9.13
% 60.95/9.13
% 60.95/9.13 % ------
% 60.95/9.13 % Current options:
% 60.95/9.13 % ------
% 60.95/9.13
% 60.95/9.13
% 60.95/9.13 %
% 60.95/9.13
% 60.95/9.13 % ------ Proving...
% 60.95/9.13 %
% 60.95/9.13
% 60.95/9.13 % SZS status Unsatisfiable for theBenchmark.p
% 60.95/9.13
% 60.95/9.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 60.95/9.14
% 60.95/9.14
%------------------------------------------------------------------------------