%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET926+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 02:49:08 PM UTC 2026
% Result : Theorem 1.60s 1.27s
% Output : CNFRefutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 11 unt; 2 def)
% Number of atoms : 70 ( 38 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 40 ( 19 ~; 15 |; 4 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 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 : 26 ( 0 sgn 24 !; 2 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
<=> ~ in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(f4,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f7,conjecture,
! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
| set_difference(singleton(X0),X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
| set_difference(singleton(X0),X1) = empty_set ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0,X1] :
( singleton(X0) != set_difference(singleton(X0),X1)
& empty_set != set_difference(singleton(X0),X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0,X1] :
( ( singleton(X0) != set_difference(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| set_difference(singleton(X0),X1) = singleton(X0) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f12,plain,
! [X0,X1] :
( ( empty_set != set_difference(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| set_difference(singleton(X0),X1) = empty_set ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f15,plain,
( singleton(sK2) != set_difference(singleton(sK2),sK3)
& empty_set != set_difference(singleton(sK2),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f10]) ).
fof(f19,plain,
! [X0,X1] :
( in(X0,X1)
| singleton(X0) = set_difference(singleton(X0),X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
! [X0,X1] :
( ~ in(X0,X1)
| empty_set = set_difference(singleton(X0),X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
singleton(sK2) != set_difference(singleton(sK2),sK3),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
empty_set != set_difference(singleton(sK2),sK3),
inference(cnf_transformation,[],[f15]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(singleton(X0),X1) = singleton(X0) ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( set_difference(singleton(X0),X1) = empty_set )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_57,negated_conjecture,
set_difference(singleton(sK2),sK3) != empty_set,
inference(cnf_transformation,[],[f25]) ).
tcf(c_58,negated_conjecture,
set_difference(singleton(sK2),sK3) != singleton(sK2),
inference(cnf_transformation,[],[f24]) ).
tcf(c_154,definition,
iPr_def_10 = singleton(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_155,definition,
iPr_def_11 = set_difference(iPr_def_10,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_156,negated_conjecture,
iPr_def_11 != iPr_def_10,
inference(demodulation,[status(thm)],[c_58,c_154,c_155]) ).
tcf(c_157,negated_conjecture,
iPr_def_11 != empty_set,
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_386,plain,
! [X0: $i,X1: $i] :
( ( set_difference(singleton(X0),X1) = empty_set )
| ( set_difference(singleton(X0),X1) = singleton(X0) ) ),
inference(superposition,[status(thm)],[c_51,c_53]) ).
tcf(c_440,plain,
! [X0: $i] :
( ( set_difference(iPr_def_10,X0) = iPr_def_10 )
| ( set_difference(singleton(sK2),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_154,c_386]) ).
tcf(c_443,plain,
! [X0: $i] :
( ( set_difference(iPr_def_10,X0) = iPr_def_10 )
| ( set_difference(iPr_def_10,X0) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_440,c_154]) ).
tcf(c_455,plain,
( ( empty_set = iPr_def_11 )
| ( set_difference(iPr_def_10,sK3) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_155,c_443]) ).
tcf(c_461,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( empty_set = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_455,c_155]) ).
tcf(c_475,plain,
iPr_def_10 = iPr_def_11,
inference(superposition,[status(thm)],[c_461,c_157]) ).
tcf(c_480,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_156,c_475]) ).
tcf(c_481,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_480]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET926+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n008.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:23:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 1.60/1.27 % SZS status Started for theBenchmark.p
% 1.60/1.27 % SZS status Theorem for theBenchmark.p
% 1.60/1.27
% 1.60/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.60/1.27
% 1.60/1.27 % ------ iProver source info
% 1.60/1.27
% 1.60/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.60/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.60/1.27 % git: non_committed_changes: false
% 1.60/1.27
% 1.60/1.27 % ------ Parsing...
% 1.60/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.60/1.27
% 1.60/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.60/1.27
% 1.60/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.60/1.27
% 1.60/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.60/1.27 % ------ Proving...
% 1.60/1.27 % ------ Problem Properties
% 1.60/1.27
% 1.60/1.27 %
% 1.60/1.27 % clauses 12
% 1.60/1.27 % conjectures 2
% 1.60/1.27 % EPR 6
% 1.60/1.27 % Horn 11
% 1.60/1.27 % unary 7
% 1.60/1.27 % binary 5
% 1.60/1.27 % lits 17
% 1.60/1.27 % lits eq 8
% 1.60/1.27 % fd_pure 0
% 1.60/1.27 % fd_pseudo 0
% 1.60/1.27 % fd_cond 0
% 1.60/1.27 % fd_pseudo_cond 0
% 1.60/1.27 % AC symbols 0
% 1.60/1.27
% 1.60/1.27 % ------ Schedule dynamic 5 is on
% 1.60/1.27
% 1.60/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.60/1.27
% 1.60/1.27
% 1.60/1.27 % ------
% 1.60/1.27 % Current options:
% 1.60/1.27 % ------
% 1.60/1.27
% 1.60/1.27
% 1.60/1.27 %
% 1.60/1.27
% 1.60/1.27 % ------ Proving...
% 1.60/1.27 %
% 1.60/1.27
% 1.60/1.27 % SZS status Theorem for theBenchmark.p
% 1.60/1.27
% 1.60/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.60/1.27
% 1.60/1.27
%------------------------------------------------------------------------------