%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU186+1 : TPTP v9.3.1. Released v3.3.0.
% 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 02:55:48 PM UTC 2026
% Result : Theorem 2.74s 11.48s
% Output : CNFRefutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 25 unt; 0 def)
% Number of atoms : 100 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 92 ( 44 ~; 32 |; 8 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 75 !; 5 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : X1 != ordered_pair(X2,X3)
& in(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f11,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f22,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f23,conjecture,
! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f24,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f28,plain,
! [X0] :
( relation(X0)
=> ! [X1] :
~ ( ! [X2,X3] : X1 != ordered_pair(X2,X3)
& in(X1,X0) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f31,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f33,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f34,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
? [X0] :
( relation(X0)
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& empty_set != X0 ),
inference(ennf_transformation,[],[f24]) ).
fof(f36,plain,
? [X0] :
( relation(X0)
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& empty_set != X0 ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f25]) ).
fof(f40,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ordered_pair(sK0(X1),sK1(X1)) = X1
| ~ in(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X1)),skolemize(X3,sK1(X1))],[f31]) ).
fof(f41,plain,
! [X0] : element(sK2(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f11]) ).
fof(f46,plain,
( relation(sK7)
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),sK7)
& empty_set != sK7 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f36]) ).
fof(f49,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f50,plain,
! [X0,X1] :
( ~ relation(X0)
| ordered_pair(sK0(X1),sK1(X1)) = X1
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f51,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0] : element(sK2(X0),X0),
inference(cnf_transformation,[],[f41]) ).
fof(f66,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f67,plain,
relation(sK7),
inference(cnf_transformation,[],[f46]) ).
fof(f68,plain,
! [X2,X1] : ~ in(ordered_pair(X1,X2),sK7),
inference(cnf_transformation,[],[f46]) ).
fof(f69,plain,
empty_set != sK7,
inference(cnf_transformation,[],[f46]) ).
fof(f70,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f73,plain,
! [X0,X1] :
( ~ relation(X0)
| unordered_pair(unordered_pair(sK0(X1),sK1(X1)),singleton(sK0(X1))) = X1
| ~ in(X1,X0) ),
inference(definition_unfolding,[],[f50,f51]) ).
fof(f75,plain,
! [X2,X1] : ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),sK7),
inference(definition_unfolding,[],[f68,f51]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f49]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK0(X0),sK1(X0)),singleton(sK0(X0))) = X0 )
| ~ relation(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_53,plain,
! [X0: $i] : element(sK2(X0),X0),
inference(cnf_transformation,[],[f52]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_68,negated_conjecture,
empty_set != sK7,
inference(cnf_transformation,[],[f69]) ).
tcf(c_69,negated_conjecture,
! [X0: $i,X1: $i] : ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK7),
inference(cnf_transformation,[],[f75]) ).
tcf(c_70,negated_conjecture,
relation(sK7),
inference(cnf_transformation,[],[f67]) ).
tcf(c_71,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7),
inference(demodulation,[status(thm)],[c_69,c_51]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(singleton(sK0(X0)),unordered_pair(sK0(X0),sK1(X0))) = X0 )
| ~ relation(X1)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_52,c_51]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| in(X1,X2)
| ( X0 != X2 )
| ( sK2(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_67]) ).
tcf(c_206,plain,
! [X0: $i] :
( empty(X0)
| in(sK2(X0),X0) ),
inference(unflattening,[status(thm)],[c_205]) ).
tcf(c_400,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7),
inference(demodulation,[status(thm)],[c_170]) ).
tcf(c_401,negated_conjecture,
relation(sK7),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_402,negated_conjecture,
empty_set != sK7,
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_626,plain,
! [X0: $i] :
( empty(X0)
| ( unordered_pair(singleton(sK0(sK2(X0))),unordered_pair(sK0(sK2(X0)),sK1(sK2(X0)))) = sK2(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_206,c_183]) ).
tcf(c_671,plain,
( empty(sK7)
| ( unordered_pair(singleton(sK0(sK2(sK7))),unordered_pair(sK0(sK2(sK7)),sK1(sK2(sK7)))) = sK2(sK7) ) ),
inference(superposition,[status(thm)],[c_401,c_626]) ).
tcf(c_693,plain,
( ( empty_set = sK7 )
| ( unordered_pair(singleton(sK0(sK2(sK7))),unordered_pair(sK0(sK2(sK7)),sK1(sK2(sK7)))) = sK2(sK7) ) ),
inference(superposition,[status(thm)],[c_671,c_71]) ).
tcf(c_695,plain,
unordered_pair(singleton(sK0(sK2(sK7))),unordered_pair(sK0(sK2(sK7)),sK1(sK2(sK7)))) = sK2(sK7),
inference(forward_subsumption_resolution,[status(thm)],[c_693,c_402]) ).
tcf(c_699,plain,
~ in(sK2(sK7),sK7),
inference(superposition,[status(thm)],[c_695,c_400]) ).
tcf(c_700,plain,
empty(sK7),
inference(superposition,[status(thm)],[c_206,c_699]) ).
tcf(c_704,plain,
empty_set = sK7,
inference(superposition,[status(thm)],[c_700,c_71]) ).
tcf(c_706,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_704,c_402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU186+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.40 % Computer : n019.cluster.edu
% 0.11/10.40 % Model : x86_64 x86_64
% 0.11/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.40 % Memory : 8046.5625MB
% 0.11/10.40 % OS : Linux 6.8.0-71-generic
% 0.15/10.40 % CPULimit : 300
% 0.15/10.40 % WCLimit : 300
% 0.15/10.40 % DateTime : Thu Sep 24 13:06:16 UTC 2026
% 0.15/10.40 % CPUTime :
% 0.15/10.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.46 Running first-order theorem proving
% 0.15/10.47 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
% 0.15/10.48
% 0.15/10.48 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.48
% 0.15/10.48 % Detected problem language: tptp
% 0.16/10.50 % Proving...
% 2.74/11.48 % SZS status Started for theBenchmark.p
% 2.74/11.48 % SZS status Theorem for theBenchmark.p
% 2.74/11.48
% 2.74/11.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.74/11.48
% 2.74/11.48 % ------ iProver source info
% 2.74/11.48
% 2.74/11.48 % git: date: 2026-07-19 20:42:38 +0200
% 2.74/11.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.74/11.48 % git: non_committed_changes: false
% 2.74/11.48
% 2.74/11.48 % ------ Parsing...
% 2.74/11.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.74/11.48
% 2.74/11.48 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.74/11.48
% 2.74/11.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.74/11.48
% 2.74/11.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.74/11.48 % ------ Proving...
% 2.74/11.48 % ------ Problem Properties
% 2.74/11.48
% 2.74/11.48 %
% 2.74/11.48 % clauses 21
% 2.74/11.48 % conjectures 2
% 2.74/11.48 % EPR 15
% 2.74/11.48 % Horn 20
% 2.74/11.48 % unary 14
% 2.74/11.48 % binary 5
% 2.74/11.48 % lits 30
% 2.74/11.48 % lits eq 5
% 2.74/11.48 % fd_pure 0
% 2.74/11.48 % fd_pseudo 0
% 2.74/11.48 % fd_cond 1
% 2.74/11.48 % fd_pseudo_cond 1
% 2.74/11.48 % AC symbols 0
% 2.74/11.48
% 2.74/11.48 % ------ Schedule dynamic 5 is on
% 2.74/11.48
% 2.74/11.48 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.74/11.48
% 2.74/11.48
% 2.74/11.48 % ------
% 2.74/11.48 % Current options:
% 2.74/11.48 % ------
% 2.74/11.48
% 2.74/11.48
% 2.74/11.48 %
% 2.74/11.48
% 2.74/11.48 % ------ Proving...
% 2.74/11.48 %
% 2.74/11.48
% 2.74/11.48 % SZS status Theorem for theBenchmark.p
% 2.74/11.48
% 2.74/11.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.74/11.48
% 2.74/11.48
%------------------------------------------------------------------------------