%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET886+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 02:48:53 PM UTC 2026
% Result : Theorem 0.18s 1.21s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 21 unt; 2 def)
% Number of atoms : 65 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 9 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 34 !; 3 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),singleton(X2))
=> X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),singleton(X2))
=> unordered_pair(X0,X1) = singleton(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),singleton(X2))
=> unordered_pair(X0,X1) = singleton(X2) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f10,plain,
! [X0,X1,X2] :
( ~ subset(unordered_pair(X0,X1),singleton(X2))
| X0 = X2 ),
inference(ennf_transformation,[],[f5]) ).
fof(f11,plain,
? [X0,X1,X2] :
( subset(unordered_pair(X0,X1),singleton(X2))
& unordered_pair(X0,X1) != singleton(X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f14,plain,
( subset(unordered_pair(sK2,sK3),singleton(sK4))
& unordered_pair(sK2,sK3) != singleton(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f11]) ).
fof(f15,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),singleton(X2))
| X0 = X2 ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
subset(unordered_pair(sK2,sK3),singleton(sK4)),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
unordered_pair(sK2,sK3) != singleton(sK4),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),unordered_pair(X2,X2))
| X0 = X2 ),
inference(definition_unfolding,[],[f19,f22]) ).
fof(f24,plain,
unordered_pair(sK2,sK3) != unordered_pair(sK4,sK4),
inference(definition_unfolding,[],[f21,f22]) ).
fof(f25,plain,
subset(unordered_pair(sK2,sK3),unordered_pair(sK4,sK4)),
inference(definition_unfolding,[],[f20,f22]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f15]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ subset(unordered_pair(X0,X1),unordered_pair(X2,X2)) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_54,negated_conjecture,
unordered_pair(sK2,sK3) != unordered_pair(sK4,sK4),
inference(cnf_transformation,[],[f24]) ).
tcf(c_55,negated_conjecture,
subset(unordered_pair(sK2,sK3),unordered_pair(sK4,sK4)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_156,definition,
iPr_def_10 = unordered_pair(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_157,definition,
iPr_def_11 = unordered_pair(sK4,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_158,negated_conjecture,
subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_55,c_157,c_156]) ).
tcf(c_159,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ subset(unordered_pair(X0,X1),unordered_pair(X2,X2)) ),
inference(superposition,[status(thm)],[c_49,c_53]) ).
tcf(c_254,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ subset(iPr_def_10,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_156,c_53]) ).
tcf(c_273,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ~ subset(iPr_def_10,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_156,c_252]) ).
tcf(c_285,plain,
( ( sK2 = sK4 )
| ~ subset(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_157,c_254]) ).
tcf(c_286,plain,
sK2 = sK4,
inference(forward_subsumption_resolution,[status(thm)],[c_285,c_158]) ).
tcf(c_288,plain,
unordered_pair(sK4,sK3) = iPr_def_10,
inference(demodulation,[status(thm)],[c_156,c_286]) ).
tcf(c_310,plain,
( ( sK3 = sK4 )
| ~ subset(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_157,c_273]) ).
tcf(c_311,plain,
sK3 = sK4,
inference(forward_subsumption_resolution,[status(thm)],[c_310,c_158]) ).
tcf(c_313,plain,
unordered_pair(sK4,sK4) = iPr_def_10,
inference(demodulation,[status(thm)],[c_288,c_311]) ).
tcf(c_314,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_157,c_313]) ).
tcf(c_315,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_314,c_159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET886+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.55 % Computer : n012.cluster.edu
% 0.04/0.55 % Model : x86_64 x86_64
% 0.04/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.55 % Memory : 8046.5625MB
% 0.04/0.55 % OS : Linux 6.8.0-71-generic
% 0.04/0.55 % CPULimit : 300
% 0.04/0.55 % WCLimit : 300
% 0.04/0.55 % DateTime : Thu Sep 24 12:19:50 UTC 2026
% 0.04/0.55 % CPUTime :
% 0.04/0.55 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.57 Running first-order theorem proving
% 0.04/0.57 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
% 0.04/0.58
% 0.04/0.58 % ======== iProver multi-core TPTP/SMT =========
% 0.04/0.58
% 0.04/0.58 % Detected problem language: tptp
% 0.04/0.59 % Proving...
% 0.18/1.21 % SZS status Started for theBenchmark.p
% 0.18/1.21 % SZS status Theorem for theBenchmark.p
% 0.18/1.21
% 0.18/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.18/1.21
% 0.18/1.21 % ------ iProver source info
% 0.18/1.21
% 0.18/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 0.18/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.18/1.21 % git: non_committed_changes: false
% 0.18/1.21
% 0.18/1.21 % ------ Parsing...
% 0.18/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.18/1.21
% 0.18/1.21 % ------ Preprocessing... sup_sim: 0 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 %
% 0.18/1.21
% 0.18/1.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.18/1.21
% 0.18/1.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.18/1.21 % ------ Proving...
% 0.18/1.21 % ------ Problem Properties
% 0.18/1.21
% 0.18/1.21 %
% 0.18/1.21 % clauses 8
% 0.18/1.21 % conjectures 2
% 0.18/1.21 % EPR 4
% 0.18/1.21 % Horn 8
% 0.18/1.21 % unary 7
% 0.18/1.21 % binary 1
% 0.18/1.21 % lits 9
% 0.18/1.21 % lits eq 6
% 0.18/1.21 % fd_pure 0
% 0.18/1.21 % fd_pseudo 0
% 0.18/1.21 % fd_cond 0
% 0.18/1.21 % fd_pseudo_cond 1
% 0.18/1.21 % AC symbols 0
% 0.18/1.21
% 0.18/1.21 % ------ Schedule dynamic 5 is on
% 0.18/1.21
% 0.18/1.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.18/1.21
% 0.18/1.21
% 0.18/1.21 % ------
% 0.18/1.21 % Current options:
% 0.18/1.21 % ------
% 0.18/1.21
% 0.18/1.21
% 0.18/1.21 %
% 0.18/1.21
% 0.18/1.21 % ------ Proving...
% 0.18/1.21 %
% 0.18/1.21
% 0.18/1.21 % SZS status Theorem for theBenchmark.p
% 0.18/1.21
% 0.18/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.18/1.21
% 0.18/1.21
%------------------------------------------------------------------------------