%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET907+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 2.29s 16.51s
% Output : CNFRefutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 21 unt; 2 def)
% Number of atoms : 83 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 58 ( 25 ~; 16 |; 13 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 36 !; 6 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f10,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( ( in(X2,X1)
& in(X0,X1) )
=> set_union2(unordered_pair(X0,X2),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_zfmisc_1) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( in(X2,X1)
& in(X0,X1) )
=> set_union2(unordered_pair(X0,X2),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(ennf_transformation,[],[f10]) ).
fof(f20,plain,
? [X0,X1,X2] :
( in(X2,X1)
& in(X0,X1)
& set_union2(unordered_pair(X0,X2),X1) != X1 ),
inference(ennf_transformation,[],[f13]) ).
fof(f21,plain,
? [X0,X1,X2] :
( in(X2,X1)
& in(X0,X1)
& set_union2(unordered_pair(X0,X2),X1) != X1 ),
inference(flattening,[],[f20]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ~ subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( ~ subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
( in(sK4,sK3)
& in(sK2,sK3)
& sK3 != set_union2(unordered_pair(sK2,sK4),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f21]) ).
fof(f29,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
in(sK4,sK3),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
in(sK2,sK3),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
sK3 != set_union2(unordered_pair(sK2,sK4),sK3),
inference(cnf_transformation,[],[f26]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f29]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(unordered_pair(X2,X0),X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_62,negated_conjecture,
set_union2(unordered_pair(sK2,sK4),sK3) != sK3,
inference(cnf_transformation,[],[f42]) ).
tcf(c_63,negated_conjecture,
in(sK2,sK3),
inference(cnf_transformation,[],[f41]) ).
tcf(c_64,negated_conjecture,
in(sK4,sK3),
inference(cnf_transformation,[],[f40]) ).
tcf(c_130,plain,
set_union2(sK3,unordered_pair(sK2,sK4)) != sK3,
inference(demodulation,[status(thm)],[c_62,c_51]) ).
tcf(c_222,definition,
iPr_def_10 = unordered_pair(sK2,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_223,definition,
iPr_def_11 = set_union2(sK3,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_224,plain,
iPr_def_11 != sK3,
inference(demodulation,[status(thm)],[c_130,c_222,c_223]) ).
tcf(c_225,negated_conjecture,
in(sK4,sK3),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_226,negated_conjecture,
in(sK2,sK3),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_423,plain,
set_union2(iPr_def_10,sK3) = iPr_def_11,
inference(demodulation,[status(thm)],[c_223,c_51]) ).
tcf(c_503,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ~ in(sK4,X0)
| ~ in(sK2,X0) ),
inference(superposition,[status(thm)],[c_222,c_59]) ).
tcf(c_533,plain,
( subset(iPr_def_10,sK3)
| ~ in(sK4,sK3) ),
inference(superposition,[status(thm)],[c_226,c_503]) ).
tcf(c_537,plain,
subset(iPr_def_10,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_533,c_225]) ).
tcf(c_544,plain,
set_union2(iPr_def_10,sK3) = sK3,
inference(superposition,[status(thm)],[c_537,c_58]) ).
tcf(c_547,plain,
sK3 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_544,c_423]) ).
tcf(c_553,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_224,c_547]) ).
tcf(c_556,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_553]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET907+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/15.59 % CPULimit : 300
% 0.07/15.59 % WCLimit : 300
% 0.07/15.59 % DateTime : Thu Sep 24 12:21:29 UTC 2026
% 0.07/15.59 % CPUTime :
% 0.07/15.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.34/15.63 Running first-order theorem proving
% 0.34/15.63 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
% 0.34/15.64
% 0.34/15.64 % ======== iProver multi-core TPTP/SMT =========
% 0.34/15.64
% 0.34/15.64 % Detected problem language: tptp
% 0.34/15.66 % Proving...
% 2.29/16.51 % SZS status Started for theBenchmark.p
% 2.29/16.51 % SZS status Theorem for theBenchmark.p
% 2.29/16.51
% 2.29/16.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.29/16.51
% 2.29/16.51 % ------ iProver source info
% 2.29/16.51
% 2.29/16.51 % git: date: 2026-07-19 20:42:38 +0200
% 2.29/16.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.29/16.51 % git: non_committed_changes: false
% 2.29/16.51
% 2.29/16.51 % ------ Parsing...
% 2.29/16.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.29/16.51
% 2.29/16.51 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.29/16.51
% 2.29/16.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.29/16.51
% 2.29/16.51 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.29/16.51 % ------ Proving...
% 2.29/16.51 % ------ Problem Properties
% 2.29/16.51
% 2.29/16.51 %
% 2.29/16.51 % clauses 18
% 2.29/16.51 % conjectures 2
% 2.29/16.51 % EPR 7
% 2.29/16.51 % Horn 18
% 2.29/16.51 % unary 11
% 2.29/16.51 % binary 6
% 2.29/16.51 % lits 26
% 2.29/16.51 % lits eq 7
% 2.29/16.51 % fd_pure 0
% 2.29/16.51 % fd_pseudo 0
% 2.29/16.51 % fd_cond 0
% 2.29/16.51 % fd_pseudo_cond 0
% 2.29/16.51 % AC symbols 0
% 2.29/16.51
% 2.29/16.51 % ------ Schedule dynamic 5 is on
% 2.29/16.51
% 2.29/16.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.29/16.51
% 2.29/16.51
% 2.29/16.51 % ------
% 2.29/16.51 % Current options:
% 2.29/16.51 % ------
% 2.29/16.51
% 2.29/16.51
% 2.29/16.51 %
% 2.29/16.51
% 2.29/16.51 % ------ Proving...
% 2.29/16.51 %
% 2.29/16.51
% 2.29/16.51 % SZS status Theorem for theBenchmark.p
% 2.29/16.51
% 2.29/16.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.29/16.51
% 2.29/16.51
%------------------------------------------------------------------------------