%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET072-7 : 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 02:46:24 PM UTC 2026
% Result : Unsatisfiable 3.86s 1.17s
% Output : CNFRefutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 16 unt; 0 def)
% Number of atoms : 48 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 17 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 40 !; 0 ?; 14 :)
% 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(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(f103,axiom,
! [X2,X3,X0,X1] :
( member(X0,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
fof(f104,axiom,
! [X2,X3,X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
fof(f127,negated_conjecture,
unordered_pair(x,z) = unordered_pair(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_1) ).
fof(f128,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_2) ).
fof(f129,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_3) ).
fof(f130,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(f131,plain,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f128,f130]) ).
fof(f139,plain,
! [X2,X3,X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f104,f130]) ).
fof(f140,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,f130]) ).
tcf(c_166,negated_conjecture,
unordered_pair(x,z) = unordered_pair(y,z),
inference(cnf_transformation,[],[f127]) ).
tcf(c_167,negated_conjecture,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f131]) ).
tcf(c_168,negated_conjecture,
x != y,
inference(cnf_transformation,[],[f129]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_183,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,[],[f140]) ).
tcf(c_947,plain,
( member(y,unordered_pair(x,z))
| ~ member(y,universal_class) ),
inference(superposition,[status(thm)],[c_166,c_180]) ).
tcf(c_1089,plain,
member(y,universal_class),
inference(superposition,[status(thm)],[c_167,c_182]) ).
tcf(c_1098,plain,
member(y,unordered_pair(x,z)),
inference(backward_subsumption_resolution,[status(thm)],[c_947,c_1089]) ).
tcf(c_1103,plain,
( ( z = y )
| ( x = y ) ),
inference(superposition,[status(thm)],[c_1098,c_181]) ).
tcf(c_1104,plain,
z = y,
inference(forward_subsumption_resolution,[status(thm)],[c_1103,c_168]) ).
tcf(c_1109,plain,
unordered_pair(x,y) = unordered_pair(y,y),
inference(demodulation,[status(thm)],[c_166,c_1104]) ).
tcf(c_1126,plain,
! [X0: $i] :
( ( X0 = y )
| ~ member(X0,unordered_pair(x,y)) ),
inference(superposition,[status(thm)],[c_1109,c_181]) ).
tcf(c_1179,plain,
( ( x = y )
| ~ member(x,universal_class) ),
inference(superposition,[status(thm)],[c_180,c_1126]) ).
tcf(c_1182,plain,
~ member(x,universal_class),
inference(forward_subsumption_resolution,[status(thm)],[c_1179,c_168]) ).
tcf(c_1583,plain,
( member(x,universal_class)
| ~ member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(universal_class,universal_class)) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_1584,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1583,c_1182,c_167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET072-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 09:38:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 3.86/1.17 % SZS status Started for theBenchmark.p
% 3.86/1.17 % SZS status Unsatisfiable for theBenchmark.p
% 3.86/1.17
% 3.86/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.86/1.17
% 3.86/1.17 % ------ iProver source info
% 3.86/1.17
% 3.86/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 3.86/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.86/1.17 % git: non_committed_changes: false
% 3.86/1.17
% 3.86/1.17 % ------ Parsing...% successful
% 3.86/1.17
% 3.86/1.17
% 3.86/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.86/1.17
% 3.86/1.17 % ------ 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 %
% 3.86/1.17
% 3.86/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.86/1.17
% 3.86/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.86/1.17 % ------ Proving...
% 3.86/1.17 % ------ Problem Properties
% 3.86/1.17
% 3.86/1.17 %
% 3.86/1.17 % clauses 30
% 3.86/1.17 % conjectures 3
% 3.86/1.17 % EPR 10
% 3.86/1.17 % Horn 26
% 3.86/1.17 % unary 12
% 3.86/1.17 % binary 11
% 3.86/1.17 % lits 55
% 3.86/1.17 % lits eq 12
% 3.86/1.17 % fd_pure 0
% 3.86/1.17 % fd_pseudo 0
% 3.86/1.17 % fd_cond 1
% 3.86/1.17 % fd_pseudo_cond 3
% 3.86/1.17 % AC symbols 0
% 3.86/1.17
% 3.86/1.17 % ------ Schedule dynamic 5 is on
% 3.86/1.17
% 3.86/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.86/1.17
% 3.86/1.17
% 3.86/1.17 % ------
% 3.86/1.17 % Current options:
% 3.86/1.17 % ------
% 3.86/1.17
% 3.86/1.17
% 3.86/1.17 %
% 3.86/1.17
% 3.86/1.17 % ------ Proving...
% 3.86/1.17 %
% 3.86/1.17
% 3.86/1.17 % SZS status Unsatisfiable for theBenchmark.p
% 3.86/1.17
% 3.86/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.86/1.17
% 3.86/1.17
%------------------------------------------------------------------------------