%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET230-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 02:46:58 PM UTC 2026
% Result : Unsatisfiable 1.54s 16.94s
% Output : CNFRefutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 73 ( 11 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 68 ( 30 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 61 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
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(f14,axiom,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
fof(f122,negated_conjecture,
cross_product(u,u) = cross_product(w,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_cross_product_cancellation_1) ).
fof(f123,negated_conjecture,
u != w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_cross_product_cancellation_2) ).
fof(f128,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(f137,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,f128]) ).
fof(f139,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(definition_unfolding,[],[f16,f128]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_174,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,[],[f137]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_256,negated_conjecture,
cross_product(u,u) = cross_product(w,w),
inference(cnf_transformation,[],[f122]) ).
tcf(c_257,negated_conjecture,
u != w,
inference(cnf_transformation,[],[f123]) ).
tcf(c_3183,plain,
! [X0: $i,X1: $i] :
( member(X0,u)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(w,w)) ),
inference(superposition,[status(thm)],[c_256,c_174]) ).
tcf(c_3194,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(w,w))
| ~ member(X1,u)
| ~ member(X0,u) ),
inference(superposition,[status(thm)],[c_256,c_176]) ).
tcf(c_3198,plain,
! [X0: $i,X1: $i] :
( member(X0,u)
| ~ member(X1,w)
| ~ member(X0,w) ),
inference(superposition,[status(thm)],[c_176,c_3183]) ).
tcf(c_3214,plain,
! [X0: $i,X1: $i] :
( member(X0,w)
| ~ member(X1,u)
| ~ member(X0,u) ),
inference(superposition,[status(thm)],[c_3194,c_174]) ).
tcf(c_3377,plain,
( ( u = w )
| ~ subclass(w,u)
| ~ subclass(u,w) ),
inference(instantiation,[status(thm)],[c_169]) ).
tcf(c_3514,plain,
! [X0: $i,X1: $i] :
( subclass(u,X1)
| member(not_subclass_element(u,X1),w)
| ~ member(X0,u) ),
inference(superposition,[status(thm)],[c_164,c_3214]) ).
tcf(c_3515,plain,
! [X0: $i,X1: $i] :
( subclass(w,X1)
| member(not_subclass_element(w,X1),u)
| ~ member(X0,w) ),
inference(superposition,[status(thm)],[c_164,c_3198]) ).
tcf(c_3609,plain,
! [X0: $i,X1: $i] :
( subclass(u,X1)
| subclass(u,X0)
| member(not_subclass_element(u,X0),w) ),
inference(superposition,[status(thm)],[c_164,c_3514]) ).
tcf(c_3617,plain,
! [X0: $i,X1: $i] :
( subclass(w,X1)
| subclass(w,X0)
| member(not_subclass_element(w,X0),u) ),
inference(superposition,[status(thm)],[c_164,c_3515]) ).
tcf(c_3627,plain,
! [X0: $i] :
( subclass(u,w)
| subclass(u,X0) ),
inference(superposition,[status(thm)],[c_3609,c_165]) ).
tcf(c_3660,plain,
! [X0: $i] :
( subclass(w,u)
| subclass(w,X0) ),
inference(superposition,[status(thm)],[c_3617,c_165]) ).
tcf(c_3754,plain,
! [X0: $i] :
( subclass(u,X0)
| ( u = w )
| ~ subclass(w,u) ),
inference(superposition,[status(thm)],[c_3627,c_169]) ).
tcf(c_3759,plain,
subclass(u,w),
inference(equality_factoring,[status(thm)],[c_3627]) ).
tcf(c_3768,plain,
~ subclass(w,u),
inference(global_subsumption_just,[status(thm)],[c_3754,c_257,c_3377,c_3759]) ).
tcf(c_3773,plain,
! [X0: $i] : subclass(w,X0),
inference(backward_subsumption_resolution,[status(thm)],[c_3660,c_3768]) ).
tcf(c_3855,plain,
$false,
inference(superposition,[status(thm)],[c_3773,c_3768]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET230-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/15.56 % CPULimit : 300
% 0.10/15.56 % WCLimit : 300
% 0.10/15.56 % DateTime : Thu Sep 24 10:19:39 UTC 2026
% 0.10/15.56 % CPUTime :
% 0.10/15.56 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.22/15.60 Running first-order theorem proving
% 0.22/15.60 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
% 0.22/15.61
% 0.22/15.61 % ======== iProver multi-core TPTP/SMT =========
% 0.22/15.61
% 0.22/15.61 % Detected problem language: tptp
% 0.22/15.62 % Proving...
% 1.54/16.94 % SZS status Started for theBenchmark.p
% 1.54/16.94 % SZS status Unsatisfiable for theBenchmark.p
% 1.54/16.94
% 1.54/16.94 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.54/16.94
% 1.54/16.94 % ------ iProver source info
% 1.54/16.94
% 1.54/16.94 % git: date: 2026-07-19 20:42:38 +0200
% 1.54/16.94 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.54/16.94 % git: non_committed_changes: false
% 1.54/16.94
% 1.54/16.94 % ------ Parsing...% successful
% 1.54/16.94
% 1.54/16.94
% 1.54/16.94 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.54/16.94
% 1.54/16.94 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 1.54/16.94
% 1.54/16.94 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.54/16.94
% 1.54/16.94 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.54/16.94 % ------ Proving...
% 1.54/16.94 % ------ Problem Properties
% 1.54/16.94
% 1.54/16.94 %
% 1.54/16.94 % clauses 83
% 1.54/16.94 % conjectures 2
% 1.54/16.94 % EPR 13
% 1.54/16.94 % Horn 75
% 1.54/16.94 % unary 22
% 1.54/16.94 % binary 40
% 1.54/16.94 % lits 171
% 1.54/16.94 % lits eq 27
% 1.54/16.94 % fd_pure 0
% 1.54/16.94 % fd_pseudo 0
% 1.54/16.94 % fd_cond 3
% 1.54/16.94 % fd_pseudo_cond 7
% 1.54/16.94 % AC symbols 0
% 1.54/16.94
% 1.54/16.94 % ------ Input Options Time Limit: Unbounded
% 1.54/16.94
% 1.54/16.94
% 1.54/16.94 % ------
% 1.54/16.94 % Current options:
% 1.54/16.94 % ------
% 1.54/16.94
% 1.54/16.94
% 1.54/16.94 %
% 1.54/16.94
% 1.54/16.94 % ------ Proving...
% 1.54/16.94 %
% 1.54/16.94
% 1.54/16.94 % SZS status Unsatisfiable for theBenchmark.p
% 1.54/16.94
% 1.54/16.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.54/16.94
% 1.54/16.94
%------------------------------------------------------------------------------