%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET119-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 02:46:40 PM UTC 2026
% Result : Unsatisfiable 3.87s 6.75s
% Output : CNFRefutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 20 unt; 0 def)
% Number of atoms : 58 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 33 ( 14 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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; 4 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f103,axiom,
! [X2,X3,X0,X1] :
( member(X0,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
fof(f120,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f124,axiom,
! [X0,X1] :
( unordered_pair(X0,X1) = singleton(X1)
| member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton2) ).
fof(f138,axiom,
! [X0] :
( singleton(X0) = null_class
| member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f175,axiom,
! [X0] :
( first(X0) = X0
| member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_2) ).
fof(f177,axiom,
! [X0] :
( first(X0) = X0
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_4) ).
fof(f187,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_OP_determines_components1_1) ).
fof(f188,negated_conjecture,
first(ordered_pair(x,y)) != ordered_pair(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_OP_determines_components1_2) ).
fof(f189,plain,
ordered_pair(x,y) != first(ordered_pair(x,y)),
inference(reorient_equations,[],[f188]) ).
fof(f190,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(f191,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))) != first(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),
inference(definition_unfolding,[],[f189,f190,f190]) ).
fof(f197,plain,
! [X2,X3,X0,X1] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f103,f190]) ).
fof(f208,plain,
! [X0] :
( first(X0) = X0
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f177,f190]) ).
fof(f210,plain,
! [X0] :
( first(X0) = X0
| member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f175,f190]) ).
fof(f217,plain,
! [X0] :
( unordered_pair(X0,X0) = null_class
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f138,f12]) ).
fof(f237,plain,
! [X0,X1] :
( unordered_pair(X0,X1) = unordered_pair(X1,X1)
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f124,f12]) ).
tcf(c_216,negated_conjecture,
~ member(x,universal_class),
inference(cnf_transformation,[],[f187]) ).
tcf(c_217,negated_conjecture,
first(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
inference(cnf_transformation,[],[f191]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_234,plain,
! [X0: $i] :
( ( first(X0) = X0 )
| ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_236,plain,
! [X0: $i] :
( member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class))
| ( first(X0) = X0 ) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_243,plain,
! [X0: $i] :
( member(X0,universal_class)
| ( unordered_pair(X0,X0) = null_class ) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_279,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ( unordered_pair(X0,X0) = unordered_pair(X1,X0) ) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_281,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f120]) ).
tcf(c_2091,plain,
unordered_pair(x,x) = null_class,
inference(superposition,[status(thm)],[c_243,c_216]) ).
tcf(c_2092,plain,
first(unordered_pair(null_class,unordered_pair(x,unordered_pair(y,y)))) != unordered_pair(null_class,unordered_pair(x,unordered_pair(y,y))),
inference(demodulation,[status(thm)],[c_217,c_2091]) ).
tcf(c_2262,plain,
! [X0: $i] : unordered_pair(X0,X0) = unordered_pair(x,X0),
inference(superposition,[status(thm)],[c_279,c_216]) ).
tcf(c_2265,plain,
first(unordered_pair(null_class,unordered_pair(x,unordered_pair(x,y)))) != unordered_pair(null_class,unordered_pair(x,unordered_pair(x,y))),
inference(demodulation,[status(thm)],[c_2092,c_2262]) ).
tcf(c_2297,plain,
! [X0: $i] : unordered_pair(X0,X0) = unordered_pair(X0,x),
inference(superposition,[status(thm)],[c_2262,c_281]) ).
tcf(c_3088,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(x,universal_class)
| ~ member(unordered_pair(null_class,unordered_pair(x,unordered_pair(X0,X0))),cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_2091,c_223]) ).
tcf(c_3096,plain,
! [X0: $i,X1: $i,X2: $i] : ~ member(unordered_pair(null_class,unordered_pair(x,unordered_pair(X0,X0))),cross_product(X1,X2)),
inference(forward_subsumption_resolution,[status(thm)],[c_3088,c_216]) ).
tcf(c_3381,plain,
! [X0: $i,X1: $i,X2: $i] : ~ member(unordered_pair(null_class,unordered_pair(x,unordered_pair(x,X0))),cross_product(X1,X2)),
inference(superposition,[status(thm)],[c_2262,c_3096]) ).
tcf(c_4821,plain,
! [X0: $i] :
( ( first(X0) = X0 )
| ( unordered_pair(unordered_pair(x,first(X0)),unordered_pair(first(X0),unordered_pair(x,second(X0)))) = X0 ) ),
inference(demodulation,[status(thm)],[c_234,c_281,c_2297]) ).
tcf(c_6160,plain,
! [X0: $i] :
( member(unordered_pair(unordered_pair(x,first(X0)),unordered_pair(first(X0),unordered_pair(x,second(X0)))),cross_product(universal_class,universal_class))
| ( first(X0) = X0 ) ),
inference(demodulation,[status(thm)],[c_236,c_281,c_2297]) ).
tcf(c_6167,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ( first(X0) = X0 ) ),
inference(superposition,[status(thm)],[c_4821,c_6160]) ).
tcf(c_7959,plain,
! [X0: $i] : first(unordered_pair(null_class,unordered_pair(x,unordered_pair(x,X0)))) = unordered_pair(null_class,unordered_pair(x,unordered_pair(x,X0))),
inference(superposition,[status(thm)],[c_6167,c_3381]) ).
tcf(c_7989,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_2265,c_7959]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET119-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.37 % Computer : n019.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Thu Sep 24 09:55:24 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 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
% 0.13/5.43
% 0.13/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.43
% 0.13/5.43 % Detected problem language: tptp
% 0.13/5.44 % Proving...
% 3.87/6.75 % SZS status Started for theBenchmark.p
% 3.87/6.75 % SZS status Unsatisfiable for theBenchmark.p
% 3.87/6.75
% 3.87/6.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.87/6.75
% 3.87/6.75 % ------ iProver source info
% 3.87/6.75
% 3.87/6.75 % git: date: 2026-07-19 20:42:38 +0200
% 3.87/6.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.87/6.75 % git: non_committed_changes: false
% 3.87/6.75
% 3.87/6.75 % ------ Parsing...% successful
% 3.87/6.75
% 3.87/6.75
% 3.87/6.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.87/6.75
% 3.87/6.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.87/6.75
% 3.87/6.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.87/6.75
% 3.87/6.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.87/6.75 % ------ Proving...
% 3.87/6.75 % ------ Problem Properties
% 3.87/6.75
% 3.87/6.75 %
% 3.87/6.75 % clauses 60
% 3.87/6.75 % conjectures 2
% 3.87/6.75 % EPR 10
% 3.87/6.75 % Horn 46
% 3.87/6.75 % unary 15
% 3.87/6.75 % binary 28
% 3.87/6.75 % lits 123
% 3.87/6.75 % lits eq 44
% 3.87/6.75 % fd_pure 0
% 3.87/6.75 % fd_pseudo 0
% 3.87/6.75 % fd_cond 1
% 3.87/6.75 % fd_pseudo_cond 11
% 3.87/6.75 % AC symbols 0
% 3.87/6.75
% 3.87/6.75 % ------ Schedule dynamic 5 is on
% 3.87/6.75
% 3.87/6.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.87/6.75
% 3.87/6.75
% 3.87/6.75 % ------
% 3.87/6.75 % Current options:
% 3.87/6.75 % ------
% 3.87/6.75
% 3.87/6.75
% 3.87/6.75 %
% 3.87/6.75
% 3.87/6.75 % ------ Proving...
% 3.87/6.75 %
% 3.87/6.75
% 3.87/6.75 % SZS status Unsatisfiable for theBenchmark.p
% 3.87/6.75
% 3.87/6.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.87/6.75
% 3.87/6.75
%------------------------------------------------------------------------------