%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET633+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 02:47:38 PM UTC 2026
% Result : Theorem 1.90s 1.26s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 20 unt; 3 def)
% Number of atoms : 71 ( 9 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 42 ( 19 ~; 11 |; 9 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 32 !; 6 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(union(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_subset) ).
fof(f5,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( ( subset(difference(X1,X0),X2)
& subset(difference(X0,X1),X2) )
=> subset(symmetric_difference(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th115) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(difference(X1,X0),X2)
& subset(difference(X0,X1),X2) )
=> subset(symmetric_difference(X0,X1),X2) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(union(X0,X2),X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(union(X0,X2),X1) ),
inference(flattening,[],[f11]) ).
fof(f14,plain,
? [X0,X1,X2] :
( subset(difference(X1,X0),X2)
& subset(difference(X0,X1),X2)
& ~ subset(symmetric_difference(X0,X1),X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f15,plain,
? [X0,X1,X2] :
( subset(difference(X1,X0),X2)
& subset(difference(X0,X1),X2)
& ~ subset(symmetric_difference(X0,X1),X2) ),
inference(flattening,[],[f14]) ).
fof(f24,plain,
( subset(difference(sK3,sK2),sK4)
& subset(difference(sK2,sK3),sK4)
& ~ subset(symmetric_difference(sK2,sK3),sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f15]) ).
fof(f25,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(union(X0,X2),X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f33,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f40,plain,
subset(difference(sK3,sK2),sK4),
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
subset(difference(sK2,sK3),sK4),
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
~ subset(symmetric_difference(sK2,sK3),sK4),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
~ subset(union(difference(sK2,sK3),difference(sK3,sK2)),sK4),
inference(definition_unfolding,[],[f42,f25]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(union(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f33]) ).
tcf(c_61,negated_conjecture,
~ subset(union(difference(sK2,sK3),difference(sK3,sK2)),sK4),
inference(cnf_transformation,[],[f44]) ).
tcf(c_62,negated_conjecture,
subset(difference(sK2,sK3),sK4),
inference(cnf_transformation,[],[f41]) ).
tcf(c_63,negated_conjecture,
subset(difference(sK3,sK2),sK4),
inference(cnf_transformation,[],[f40]) ).
tcf(c_286,definition,
iPr_def_10 = difference(sK3,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_287,definition,
iPr_def_11 = difference(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_288,definition,
iPr_def_12 = union(iPr_def_11,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_289,negated_conjecture,
subset(iPr_def_10,sK4),
inference(demodulation,[status(thm)],[c_63,c_286]) ).
tcf(c_290,negated_conjecture,
subset(iPr_def_11,sK4),
inference(demodulation,[status(thm)],[c_62,c_287]) ).
tcf(c_291,negated_conjecture,
~ subset(iPr_def_12,sK4),
inference(demodulation,[status(thm)],[c_61,c_288]) ).
tcf(c_500,plain,
union(iPr_def_10,iPr_def_11) = iPr_def_12,
inference(demodulation,[status(thm)],[c_288,c_56]) ).
tcf(c_633,plain,
! [X0: $i] :
( subset(iPr_def_12,X0)
| ~ subset(iPr_def_11,X0)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_500,c_49]) ).
tcf(c_861,plain,
( subset(iPr_def_12,sK4)
| ~ subset(iPr_def_10,sK4) ),
inference(superposition,[status(thm)],[c_290,c_633]) ).
tcf(c_865,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_861,c_291,c_289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET633+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n007.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 11:28:53 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 1.90/1.26 % SZS status Started for theBenchmark.p
% 1.90/1.26 % SZS status Theorem for theBenchmark.p
% 1.90/1.26
% 1.90/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.90/1.26
% 1.90/1.26 % ------ iProver source info
% 1.90/1.26
% 1.90/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 1.90/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.90/1.26 % git: non_committed_changes: false
% 1.90/1.26
% 1.90/1.26 % ------ Parsing...
% 1.90/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.90/1.26
% 1.90/1.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.90/1.26
% 1.90/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.90/1.26
% 1.90/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.90/1.26 % ------ Proving...
% 1.90/1.26 % ------ Problem Properties
% 1.90/1.26
% 1.90/1.26 %
% 1.90/1.26 % clauses 17
% 1.90/1.26 % conjectures 3
% 1.90/1.26 % EPR 5
% 1.90/1.26 % Horn 14
% 1.90/1.26 % unary 8
% 1.90/1.26 % binary 4
% 1.90/1.26 % lits 31
% 1.90/1.26 % lits eq 6
% 1.90/1.26 % fd_pure 0
% 1.90/1.26 % fd_pseudo 0
% 1.90/1.26 % fd_cond 0
% 1.90/1.26 % fd_pseudo_cond 2
% 1.90/1.26 % AC symbols 0
% 1.90/1.26
% 1.90/1.26 % ------ Schedule dynamic 5 is on
% 1.90/1.26
% 1.90/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.90/1.26
% 1.90/1.26
% 1.90/1.26 % ------
% 1.90/1.26 % Current options:
% 1.90/1.26 % ------
% 1.90/1.26
% 1.90/1.26
% 1.90/1.26 %
% 1.90/1.26
% 1.90/1.26 % ------ Proving...
% 1.90/1.26 %
% 1.90/1.26
% 1.90/1.26 % SZS status Theorem for theBenchmark.p
% 1.90/1.26
% 1.90/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.90/1.26
% 1.90/1.26
%------------------------------------------------------------------------------