%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET911+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 : 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 02:49:05 PM UTC 2026
% Result : Theorem 1.63s 1.27s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 17 unt; 2 def)
% Number of atoms : 46 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 3 |; 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 : 20 ( 0 sgn 18 !; 2 ?; 4 :)
% 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] :
( in(X0,X1)
=> set_intersection2(X1,singleton(X0)) = singleton(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> set_intersection2(X1,singleton(X0)) = singleton(X0) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_intersection2(X1,singleton(X0)) = singleton(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_zfmisc_1) ).
fof(f11,plain,
? [X0,X1] :
( in(X0,X1)
& singleton(X0) != set_intersection2(X1,singleton(X0)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_intersection2(X1,singleton(X0)) = singleton(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f15,plain,
( in(sK2,sK3)
& singleton(sK2) != set_intersection2(sK3,singleton(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,
in(sK2,sK3),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
singleton(sK2) != set_intersection2(sK3,singleton(sK2)),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( ~ in(X0,X1)
| singleton(X0) = set_intersection2(X1,singleton(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,
set_intersection2(sK3,singleton(sK2)) != singleton(sK2),
inference(cnf_transformation,[],[f22]) ).
tcf(c_55,negated_conjecture,
in(sK2,sK3),
inference(cnf_transformation,[],[f21]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,singleton(X0)) = singleton(X0) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_128,definition,
iPr_def_10 = singleton(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_129,definition,
iPr_def_11 = set_intersection2(sK3,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_130,negated_conjecture,
in(sK2,sK3),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_131,negated_conjecture,
iPr_def_11 != iPr_def_10,
inference(demodulation,[status(thm)],[c_54,c_128,c_129]) ).
tcf(c_239,plain,
set_intersection2(iPr_def_10,sK3) = iPr_def_11,
inference(demodulation,[status(thm)],[c_129,c_49]) ).
tcf(c_247,plain,
set_intersection2(sK3,singleton(sK2)) = singleton(sK2),
inference(superposition,[status(thm)],[c_130,c_56]) ).
tcf(c_248,plain,
set_intersection2(sK3,iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_247,c_128]) ).
tcf(c_249,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_248,c_49,c_239]) ).
tcf(c_251,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_131,c_249]) ).
tcf(c_252,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET911+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:21:58 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 1.63/1.27 % SZS status Started for theBenchmark.p
% 1.63/1.27 % SZS status Theorem for theBenchmark.p
% 1.63/1.27
% 1.63/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.63/1.27
% 1.63/1.27 % ------ iProver source info
% 1.63/1.27
% 1.63/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.63/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.63/1.27 % git: non_committed_changes: false
% 1.63/1.27
% 1.63/1.27 % ------ Parsing...
% 1.63/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.63/1.27
% 1.63/1.27 % ------ 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 %
% 1.63/1.27
% 1.63/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.63/1.27
% 1.63/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.63/1.27 % ------ Proving...
% 1.63/1.27 % ------ Problem Properties
% 1.63/1.27
% 1.63/1.27 %
% 1.63/1.27 % clauses 9
% 1.63/1.27 % conjectures 2
% 1.63/1.27 % EPR 4
% 1.63/1.27 % Horn 9
% 1.63/1.27 % unary 7
% 1.63/1.27 % binary 2
% 1.63/1.27 % lits 11
% 1.63/1.27 % lits eq 7
% 1.63/1.27 % fd_pure 0
% 1.63/1.27 % fd_pseudo 0
% 1.63/1.27 % fd_cond 0
% 1.63/1.27 % fd_pseudo_cond 0
% 1.63/1.27 % AC symbols 0
% 1.63/1.27
% 1.63/1.27 % ------ Schedule dynamic 5 is on
% 1.63/1.27
% 1.63/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.63/1.27
% 1.63/1.27
% 1.63/1.27 % ------
% 1.63/1.27 % Current options:
% 1.63/1.27 % ------
% 1.63/1.27
% 1.63/1.27
% 1.63/1.27 %
% 1.63/1.27
% 1.63/1.27 % ------ Proving...
% 1.63/1.27 %
% 1.63/1.27
% 1.63/1.27 % SZS status Theorem for theBenchmark.p
% 1.63/1.27
% 1.63/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.63/1.27
% 1.63/1.27
%------------------------------------------------------------------------------