%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET017-7 : 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 : n006.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 02:46:05 PM UTC 2026
% Result : Unsatisfiable 2.82s 6.30s
% Output : CNFRefutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 20 unt; 0 def)
% Number of atoms : 52 ( 21 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 : 44 ( 0 sgn 44 !; 0 ?; 16 :)
% 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(f120,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f126,negated_conjecture,
unordered_pair(x,y) = unordered_pair(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_cancellation_1) ).
fof(f127,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_cancellation_2) ).
fof(f128,negated_conjecture,
y != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_cancellation_3) ).
fof(f129,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(f130,plain,
member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f127,f129]) ).
fof(f137,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,f129]) ).
fof(f138,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,f129]) ).
tcf(c_165,negated_conjecture,
unordered_pair(x,y) = unordered_pair(x,z),
inference(cnf_transformation,[],[f126]) ).
tcf(c_166,negated_conjecture,
member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f130]) ).
tcf(c_167,negated_conjecture,
y != z,
inference(cnf_transformation,[],[f128]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f120]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_181,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,[],[f137]) ).
tcf(c_182,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,[],[f138]) ).
tcf(c_314,plain,
unordered_pair(x,z) = unordered_pair(y,x),
inference(demodulation,[status(thm)],[c_165,c_173]) ).
tcf(c_315,plain,
unordered_pair(y,x) = unordered_pair(z,x),
inference(demodulation,[status(thm)],[c_314,c_173]) ).
tcf(c_910,plain,
( member(z,unordered_pair(y,x))
| ~ member(z,universal_class) ),
inference(superposition,[status(thm)],[c_315,c_178]) ).
tcf(c_1052,plain,
member(z,universal_class),
inference(superposition,[status(thm)],[c_166,c_181]) ).
tcf(c_1061,plain,
member(z,unordered_pair(y,x)),
inference(backward_subsumption_resolution,[status(thm)],[c_910,c_1052]) ).
tcf(c_1066,plain,
( ( y = z )
| ( x = z ) ),
inference(superposition,[status(thm)],[c_1061,c_179]) ).
tcf(c_1067,plain,
x = z,
inference(forward_subsumption_resolution,[status(thm)],[c_1066,c_167]) ).
tcf(c_1072,plain,
unordered_pair(y,z) = unordered_pair(z,z),
inference(demodulation,[status(thm)],[c_315,c_1067]) ).
tcf(c_1090,plain,
! [X0: $i] :
( ( X0 = z )
| ~ member(X0,unordered_pair(y,z)) ),
inference(superposition,[status(thm)],[c_1072,c_179]) ).
tcf(c_1139,plain,
( ( y = z )
| ~ member(y,universal_class) ),
inference(superposition,[status(thm)],[c_178,c_1090]) ).
tcf(c_1142,plain,
~ member(y,universal_class),
inference(forward_subsumption_resolution,[status(thm)],[c_1139,c_167]) ).
tcf(c_1254,plain,
( member(y,universal_class)
| ~ member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)) ),
inference(instantiation,[status(thm)],[c_182]) ).
tcf(c_1255,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1254,c_1142,c_166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET017-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n006.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 09:10:33 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.41 Running first-order theorem proving
% 0.15/5.41 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
% 0.15/5.42
% 0.15/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.42
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 2.82/6.30 % SZS status Started for theBenchmark.p
% 2.82/6.30 % SZS status Unsatisfiable for theBenchmark.p
% 2.82/6.30
% 2.82/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.82/6.30
% 2.82/6.30 % ------ iProver source info
% 2.82/6.30
% 2.82/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.82/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.82/6.30 % git: non_committed_changes: false
% 2.82/6.30
% 2.82/6.30 % ------ Parsing...% successful
% 2.82/6.30
% 2.82/6.30
% 2.82/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.82/6.30
% 2.82/6.30 % ------ Preprocessing... sup_sim: 2 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 %
% 2.82/6.30
% 2.82/6.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.82/6.30
% 2.82/6.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.82/6.30 % ------ Proving...
% 2.82/6.30 % ------ Problem Properties
% 2.82/6.30
% 2.82/6.30 %
% 2.82/6.30 % clauses 29
% 2.82/6.30 % conjectures 2
% 2.82/6.30 % EPR 10
% 2.82/6.30 % Horn 25
% 2.82/6.30 % unary 12
% 2.82/6.30 % binary 11
% 2.82/6.30 % lits 52
% 2.82/6.30 % lits eq 10
% 2.82/6.30 % fd_pure 0
% 2.82/6.30 % fd_pseudo 0
% 2.82/6.30 % fd_cond 1
% 2.82/6.30 % fd_pseudo_cond 2
% 2.82/6.30 % AC symbols 0
% 2.82/6.30
% 2.82/6.30 % ------ Schedule dynamic 5 is on
% 2.82/6.30
% 2.82/6.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.82/6.30
% 2.82/6.30
% 2.82/6.30 % ------
% 2.82/6.30 % Current options:
% 2.82/6.30 % ------
% 2.82/6.30
% 2.82/6.30
% 2.82/6.30 %
% 2.82/6.30
% 2.82/6.30 % ------ Proving...
% 2.82/6.30 %
% 2.82/6.30
% 2.82/6.30 % SZS status Unsatisfiable for theBenchmark.p
% 2.82/6.30
% 2.82/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.82/6.30
% 2.82/6.30
%------------------------------------------------------------------------------