%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET042-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 02:46:13 PM UTC 2026
% Result : Unsatisfiable 0.94s 1.30s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 80 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 97 ( 51 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
fof(f15,axiom,
! [X2,X0,X1] :
( X0 != ordered_pair(X1,X2)
| ~ little_set(X2)
| ~ little_set(X1)
| ordered_pair_predicate(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate4) ).
fof(f16,plain,
! [X2,X0,X1] :
( ordered_pair(X1,X2) != X0
| ~ little_set(X2)
| ~ little_set(X1)
| ordered_pair_predicate(X0) ),
inference(reorient_equations,[],[f15]) ).
fof(f49,axiom,
! [X2,X0,X1] :
( ~ member(second(X0),X2)
| ~ member(first(X0),X1)
| ~ ordered_pair_predicate(X0)
| ~ little_set(X0)
| member(X0,cross_product(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',cross_product4) ).
fof(f167,axiom,
! [X0,X1] :
( first(ordered_pair(X0,X1)) = X0
| ~ little_set(X1)
| ~ little_set(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_first) ).
fof(f168,axiom,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = X1
| ~ little_set(X1)
| ~ little_set(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_second) ).
fof(f173,axiom,
! [X0] :
( little_set(X0)
| ~ ordered_pair_predicate(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pairs_are_small2) ).
fof(f189,axiom,
member(a,set_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_set_a) ).
fof(f190,axiom,
member(b,set_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_set_b) ).
fof(f191,negated_conjecture,
~ member(ordered_pair(a,b),cross_product(set_a,set_b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_is_in_cross_product) ).
fof(f192,plain,
! [X2,X1] :
( ~ little_set(X2)
| ~ little_set(X1)
| ordered_pair_predicate(ordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f16]) ).
tcf(c_219,plain,
member(a,set_a),
inference(cnf_transformation,[],[f189]) ).
tcf(c_220,plain,
member(b,set_b),
inference(cnf_transformation,[],[f190]) ).
tcf(c_221,negated_conjecture,
~ member(ordered_pair(a,b),cross_product(set_a,set_b)),
inference(cnf_transformation,[],[f191]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i] :
( ordered_pair_predicate(ordered_pair(X0,X1))
| ~ little_set(X1)
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(X1,X2))
| ~ ordered_pair_predicate(X0)
| ~ little_set(X0)
| ~ member(second(X0),X2)
| ~ member(first(X0),X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i] :
( little_set(X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_233,plain,
! [X0: $i] :
( little_set(X0)
| ~ ordered_pair_predicate(X0) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] :
( ( first(ordered_pair(X0,X1)) = X0 )
| ~ little_set(X1)
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i] :
( ( second(ordered_pair(X0,X1)) = X1 )
| ~ little_set(X1)
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(X1,X2))
| ~ ordered_pair_predicate(X0)
| ~ member(first(X0),X1)
| ~ member(second(X0),X2) ),
inference(global_subsumption_just,[status(thm)],[c_228,c_233,c_228]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(X1,X2))
| ~ ordered_pair_predicate(X0)
| ~ member(second(X0),X2)
| ~ member(first(X0),X1) ),
inference(renaming,[status(thm)],[c_308]) ).
tcf(c_1998,plain,
little_set(a),
inference(superposition,[status(thm)],[c_219,c_232]) ).
tcf(c_1999,plain,
little_set(b),
inference(superposition,[status(thm)],[c_220,c_232]) ).
tcf(c_2121,plain,
! [X0: $i] :
( ( first(ordered_pair(a,X0)) = a )
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_1998,c_245]) ).
tcf(c_2148,plain,
first(ordered_pair(a,b)) = a,
inference(superposition,[status(thm)],[c_1999,c_2121]) ).
tcf(c_2171,plain,
! [X0: $i] :
( ( second(ordered_pair(a,X0)) = X0 )
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_1998,c_247]) ).
tcf(c_2280,plain,
second(ordered_pair(a,b)) = b,
inference(superposition,[status(thm)],[c_1999,c_2171]) ).
tcf(c_2477,plain,
! [X0: $i] :
( ordered_pair_predicate(ordered_pair(a,X0))
| ~ little_set(a)
| ~ little_set(X0) ),
inference(instantiation,[status(thm)],[c_225]) ).
tcf(c_3425,plain,
( ordered_pair_predicate(ordered_pair(a,b))
| ~ little_set(b)
| ~ little_set(a) ),
inference(instantiation,[status(thm)],[c_2477]) ).
tcf(c_6879,plain,
( ~ ordered_pair_predicate(ordered_pair(a,b))
| ~ member(second(ordered_pair(a,b)),set_b)
| ~ member(first(ordered_pair(a,b)),set_a) ),
inference(superposition,[status(thm)],[c_309,c_221]) ).
tcf(c_6892,plain,
( ~ member(b,set_b)
| ~ member(a,set_a)
| ~ ordered_pair_predicate(ordered_pair(a,b)) ),
inference(light_normalisation,[status(thm)],[c_6879,c_2148,c_2280]) ).
tcf(c_6893,plain,
~ ordered_pair_predicate(ordered_pair(a,b)),
inference(forward_subsumption_resolution,[status(thm)],[c_6892,c_220,c_219]) ).
tcf(c_6932,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6893,c_3425,c_1998,c_1999]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET042-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 09:27:24 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 0.94/1.30 % SZS status Started for theBenchmark.p
% 0.94/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 0.94/1.30
% 0.94/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.94/1.30
% 0.94/1.30 % ------ iProver source info
% 0.94/1.30
% 0.94/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 0.94/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.94/1.30 % git: non_committed_changes: false
% 0.94/1.30
% 0.94/1.30 % ------ Parsing...% successful
% 0.94/1.30
% 0.94/1.30
% 0.94/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.94/1.30
% 0.94/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 20 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 0.94/1.30
% 0.94/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.94/1.30
% 0.94/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.94/1.30 % ------ Proving...
% 0.94/1.30 % ------ Problem Properties
% 0.94/1.30
% 0.94/1.30 %
% 0.94/1.30 % clauses 28
% 0.94/1.30 % conjectures 1
% 0.94/1.30 % EPR 7
% 0.94/1.30 % Horn 28
% 0.94/1.30 % unary 5
% 0.94/1.30 % binary 8
% 0.94/1.30 % lits 77
% 0.94/1.30 % lits eq 8
% 0.94/1.30 % fd_pure 0
% 0.94/1.30 % fd_pseudo 0
% 0.94/1.30 % fd_cond 0
% 0.94/1.30 % fd_pseudo_cond 3
% 0.94/1.30 % AC symbols 0
% 0.94/1.30
% 0.94/1.30 % ------ Schedule dynamic 5 is on
% 0.94/1.30
% 0.94/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.94/1.30
% 0.94/1.30
% 0.94/1.30 % ------
% 0.94/1.30 % Current options:
% 0.94/1.30 % ------
% 0.94/1.30
% 0.94/1.30
% 0.94/1.30 %
% 0.94/1.30
% 0.94/1.30 % ------ Proving...
% 0.94/1.30 %
% 0.94/1.30
% 0.94/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 0.94/1.30
% 0.94/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.94/1.30
% 0.94/1.30
%------------------------------------------------------------------------------