%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET020-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 8.69s 7.39s
% Output : CNFRefutation 8.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 19 unt; 0 def)
% Number of atoms : 81 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 29 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 8 ( 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 63 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
fof(f101,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_1) ).
fof(f102,negated_conjecture,
first(ordered_pair(u,v)) != u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_2) ).
fof(f103,plain,
u != first(ordered_pair(u,v)),
inference(reorient_equations,[],[f102]) ).
fof(f108,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f114,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f14,f108]) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f15,f108]) ).
fof(f117,plain,
! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(definition_unfolding,[],[f17,f108]) ).
fof(f152,plain,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f101,f108]) ).
fof(f153,plain,
u != first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),
inference(definition_unfolding,[],[f103,f108]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f11]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_217,negated_conjecture,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f152]) ).
tcf(c_218,negated_conjecture,
first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) != u,
inference(cnf_transformation,[],[f153]) ).
tcf(c_275,plain,
member(u,universal_class),
inference(superposition,[status(thm)],[c_217,c_153]) ).
tcf(c_289,plain,
unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))) = unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),
inference(superposition,[status(thm)],[c_217,c_156]) ).
tcf(c_303,plain,
( member(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))
| ~ member(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),universal_class) ),
inference(superposition,[status(thm)],[c_289,c_150]) ).
tcf(c_305,plain,
! [X0: $i] :
( ( unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))) = X0 )
| ( unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))))) = X0 )
| ~ member(X0,unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) ),
inference(superposition,[status(thm)],[c_289,c_149]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i] :
( member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X0)
| ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_289,c_153]) ).
tcf(c_313,plain,
( member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class)
| ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)) ),
inference(instantiation,[status(thm)],[c_309]) ).
tcf(c_440,plain,
member(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),
inference(forward_subsumption_resolution,[status(thm)],[c_303,c_152]) ).
tcf(c_442,plain,
( ( unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))) = unordered_pair(u,u) )
| ( unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))) = unordered_pair(u,unordered_pair(v,v)) ) ),
inference(superposition,[status(thm)],[c_440,c_149]) ).
tcf(c_450,plain,
( ( unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))) = unordered_pair(u,u) )
| ( unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))))) = unordered_pair(u,u) )
| ~ member(unordered_pair(u,u),universal_class) ),
inference(superposition,[status(thm)],[c_150,c_305]) ).
tcf(c_1017,plain,
! [X0: $i] :
( ( first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = X0 )
| ( unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))) = unordered_pair(u,u) )
| ~ member(X0,unordered_pair(u,unordered_pair(v,v))) ),
inference(superposition,[status(thm)],[c_442,c_149]) ).
tcf(c_1040,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X2)
| ( unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))) = unordered_pair(u,u) )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(u,unordered_pair(v,v)))),cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_442,c_154]) ).
tcf(c_1219,plain,
( ( unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))) = unordered_pair(u,u) )
| ( unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))))) = unordered_pair(u,u) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_450,c_152]) ).
tcf(c_1224,plain,
( member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(u,u))
| ( unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))) = unordered_pair(u,u) )
| ~ member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class) ),
inference(superposition,[status(thm)],[c_1219,c_150]) ).
tcf(c_7317,plain,
( ( first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = u )
| ( unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))) = unordered_pair(u,u) )
| ~ member(u,universal_class) ),
inference(superposition,[status(thm)],[c_150,c_1017]) ).
tcf(c_7322,plain,
unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))) = unordered_pair(u,u),
inference(global_subsumption_just,[status(thm)],[c_1040,c_218,c_275,c_7317]) ).
tcf(c_7336,plain,
( member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(u,u))
| ~ member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class) ),
inference(superposition,[status(thm)],[c_7322,c_151]) ).
tcf(c_7886,plain,
member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(u,u)),
inference(global_subsumption_just,[status(thm)],[c_1224,c_217,c_313,c_7336]) ).
tcf(c_7899,plain,
first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = u,
inference(superposition,[status(thm)],[c_7886,c_149]) ).
tcf(c_7901,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_218,c_7899]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET020-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.37 % Computer : n002.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Thu Sep 24 09:15:54 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.41 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
% 0.15/5.44 % Proving...
% 8.69/7.39 % SZS status Started for theBenchmark.p
% 8.69/7.39 % SZS status Unsatisfiable for theBenchmark.p
% 8.69/7.39
% 8.69/7.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.69/7.39
% 8.69/7.39 % ------ iProver source info
% 8.69/7.39
% 8.69/7.39 % git: date: 2026-07-19 20:42:38 +0200
% 8.69/7.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.69/7.39 % git: non_committed_changes: false
% 8.69/7.39
% 8.69/7.39 % ------ Parsing...% successful
% 8.69/7.39
% 8.69/7.39
% 8.69/7.39 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 8.69/7.39 % ------ Proving...
% 8.69/7.39 % ------ Problem Properties
% 8.69/7.39
% 8.69/7.39 %
% 8.69/7.39 % clauses 77
% 8.69/7.39 % conjectures 2
% 8.69/7.39 % EPR 16
% 8.69/7.39 % Horn 69
% 8.69/7.39 % unary 17
% 8.69/7.39 % binary 39
% 8.69/7.39 % lits 164
% 8.69/7.39 % lits eq 21
% 8.69/7.39 % fd_pure 0
% 8.69/7.39 % fd_pseudo 0
% 8.69/7.39 % fd_cond 3
% 8.69/7.39 % fd_pseudo_cond 3
% 8.69/7.39 % AC symbols 0
% 8.69/7.39
% 8.69/7.39 % ------ Input Options Time Limit: Unbounded
% 8.69/7.39
% 8.69/7.39
% 8.69/7.39 % ------
% 8.69/7.39 % Current options:
% 8.69/7.39 % ------
% 8.69/7.39
% 8.69/7.39
% 8.69/7.39 %
% 8.69/7.39
% 8.69/7.39 % ------ Proving...
% 8.69/7.39 %
% 8.69/7.39
% 8.69/7.39 % SZS status Unsatisfiable for theBenchmark.p
% 8.69/7.39
% 8.69/7.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.69/7.39
% 8.69/7.39
%------------------------------------------------------------------------------