%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET910+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 : n020.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 02:49:05 PM UTC 2026
% Result : Theorem 0.45s 1.28s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 15 unt; 2 def)
% Number of atoms : 48 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 5 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 20 !; 2 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f6,conjecture,
! [X0,X1] :
( set_intersection2(X0,singleton(X1)) = singleton(X1)
=> in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( set_intersection2(X0,singleton(X1)) = singleton(X1)
=> in(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,axiom,
! [X0,X1] :
( set_intersection2(X0,singleton(X1)) = singleton(X1)
=> in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_zfmisc_1) ).
fof(f11,plain,
? [X0,X1] :
( set_intersection2(X0,singleton(X1)) = singleton(X1)
& ~ in(X1,X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( singleton(X1) != set_intersection2(X0,singleton(X1))
| in(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f15,plain,
( singleton(sK3) = set_intersection2(sK2,singleton(sK3))
& ~ in(sK3,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f11]) ).
fof(f16,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f21,plain,
singleton(sK3) = set_intersection2(sK2,singleton(sK3)),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
~ in(sK3,sK2),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( singleton(X1) != set_intersection2(X0,singleton(X1))
| in(X1,X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f16]) ).
tcf(c_54,negated_conjecture,
~ in(sK3,sK2),
inference(cnf_transformation,[],[f22]) ).
tcf(c_55,negated_conjecture,
set_intersection2(sK2,singleton(sK3)) = singleton(sK3),
inference(cnf_transformation,[],[f21]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( set_intersection2(X0,singleton(X1)) != singleton(X1) ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_129,definition,
iPr_def_10 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_130,definition,
iPr_def_11 = set_intersection2(sK2,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_131,negated_conjecture,
iPr_def_11 = iPr_def_10,
inference(demodulation,[status(thm)],[c_55,c_129,c_130]) ).
tcf(c_132,negated_conjecture,
~ in(sK3,sK2),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_240,plain,
set_intersection2(sK2,iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_130,c_131]) ).
tcf(c_241,plain,
set_intersection2(iPr_def_10,sK2) = iPr_def_10,
inference(demodulation,[status(thm)],[c_240,c_49]) ).
tcf(c_251,plain,
! [X0: $i] :
( in(sK3,X0)
| ( set_intersection2(X0,iPr_def_10) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_129,c_56]) ).
tcf(c_268,plain,
! [X0: $i] :
( in(sK3,X0)
| ( set_intersection2(iPr_def_10,X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_49,c_251]) ).
tcf(c_281,plain,
in(sK3,sK2),
inference(superposition,[status(thm)],[c_241,c_268]) ).
tcf(c_282,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_281,c_132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET910+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 12:22:49 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 0.45/1.28 % SZS status Started for theBenchmark.p
% 0.45/1.28 % SZS status Theorem for theBenchmark.p
% 0.45/1.28
% 0.45/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.45/1.28
% 0.45/1.28 % ------ iProver source info
% 0.45/1.28
% 0.45/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.45/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.45/1.28 % git: non_committed_changes: false
% 0.45/1.28
% 0.45/1.28 % ------ Parsing...
% 0.45/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.45/1.28
% 0.45/1.28 % ------ 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 %
% 0.45/1.28
% 0.45/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.45/1.28
% 0.45/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.45/1.28 % ------ Proving...
% 0.45/1.28 % ------ Problem Properties
% 0.45/1.28
% 0.45/1.28 %
% 0.45/1.28 % clauses 9
% 0.45/1.28 % conjectures 2
% 0.45/1.28 % EPR 4
% 0.45/1.28 % Horn 9
% 0.45/1.28 % unary 7
% 0.45/1.28 % binary 2
% 0.45/1.28 % lits 11
% 0.45/1.28 % lits eq 7
% 0.45/1.28 % fd_pure 0
% 0.45/1.28 % fd_pseudo 0
% 0.45/1.28 % fd_cond 0
% 0.45/1.28 % fd_pseudo_cond 0
% 0.45/1.28 % AC symbols 0
% 0.45/1.28
% 0.45/1.28 % ------ Schedule dynamic 5 is on
% 0.45/1.28
% 0.45/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.45/1.28
% 0.45/1.28
% 0.45/1.28 % ------
% 0.45/1.28 % Current options:
% 0.45/1.28 % ------
% 0.45/1.28
% 0.45/1.28
% 0.45/1.28 %
% 0.45/1.28
% 0.45/1.28 % ------ Proving...
% 0.45/1.28 %
% 0.45/1.28
% 0.45/1.28 % SZS status Theorem for theBenchmark.p
% 0.45/1.28
% 0.45/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.29
% 0.45/1.29
%------------------------------------------------------------------------------