%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET132-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.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 02:46:42 PM UTC 2026
% Result : Unsatisfiable 4.84s 6.77s
% Output : CNFRefutation 4.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 25
% Syntax : Number of formulae : 60 ( 37 unt; 15 def)
% Number of atoms : 153 ( 19 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 60 ( 32 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 40 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
fof(f101,axiom,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_set_builder) ).
fof(f102,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_triple3_1) ).
fof(f103,negated_conjecture,
~ member(u,set_builder(x,set_builder(y,set_builder(u,null_class)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_triple3_2) ).
fof(f109,plain,
! [X0,X1] : set_builder(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(X1))),
inference(definition_unfolding,[],[f101,f26,f12]) ).
fof(f153,plain,
~ member(u,complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(u,u)),complement(null_class)))))))))),
inference(definition_unfolding,[],[f103,f109,f109,f109]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_218,negated_conjecture,
member(u,universal_class),
inference(cnf_transformation,[],[f102]) ).
tcf(c_219,negated_conjecture,
~ member(u,complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(u,u)),complement(null_class)))))))))),
inference(cnf_transformation,[],[f153]) ).
tcf(c_2645,definition,
iPr_def_10 = unordered_pair(x,x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2646,definition,
iPr_def_11 = complement(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2647,definition,
iPr_def_12 = unordered_pair(y,y),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2648,definition,
iPr_def_13 = complement(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2649,definition,
iPr_def_14 = unordered_pair(u,u),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2650,definition,
iPr_def_15 = complement(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_2651,definition,
iPr_def_16 = complement(null_class),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_2652,definition,
iPr_def_17 = intersection(iPr_def_15,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_2653,definition,
iPr_def_18 = complement(iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_2654,definition,
iPr_def_19 = complement(iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_2655,definition,
iPr_def_20 = intersection(iPr_def_13,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_2656,definition,
iPr_def_21 = complement(iPr_def_20),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_2657,definition,
iPr_def_22 = complement(iPr_def_21),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_2658,definition,
iPr_def_23 = intersection(iPr_def_11,iPr_def_22),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_2659,definition,
iPr_def_24 = complement(iPr_def_23),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_2660,negated_conjecture,
~ member(u,iPr_def_24),
inference(demodulation,[status(thm)],[c_219,c_2651,c_2649,c_2650,c_2652,c_2653,c_2654,c_2647,c_2648,c_2655,c_2656,c_2657,c_2645,c_2646,c_2658,c_2659]) ).
tcf(c_2661,negated_conjecture,
member(u,universal_class),
inference(demodulation,[status(thm)],[c_218]) ).
tcf(c_3510,plain,
( member(u,iPr_def_14)
| ~ member(u,universal_class) ),
inference(superposition,[status(thm)],[c_2649,c_151]) ).
tcf(c_3511,plain,
member(u,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_3510,c_2661]) ).
tcf(c_3536,plain,
! [X0: $i] :
( member(X0,iPr_def_15)
| ~ member(X0,iPr_def_17) ),
inference(superposition,[status(thm)],[c_2652,c_161]) ).
tcf(c_3574,plain,
! [X0: $i] :
( member(X0,iPr_def_19)
| ~ member(X0,iPr_def_20) ),
inference(superposition,[status(thm)],[c_2655,c_162]) ).
tcf(c_3575,plain,
! [X0: $i] :
( member(X0,iPr_def_22)
| ~ member(X0,iPr_def_23) ),
inference(superposition,[status(thm)],[c_2658,c_162]) ).
tcf(c_3608,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_15)
| ~ member(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_2650,c_164]) ).
tcf(c_3610,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_19)
| ~ member(X0,iPr_def_18) ),
inference(superposition,[status(thm)],[c_2654,c_164]) ).
tcf(c_3612,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_22)
| ~ member(X0,iPr_def_21) ),
inference(superposition,[status(thm)],[c_2657,c_164]) ).
tcf(c_3828,plain,
! [X0: $i] :
( member(X0,iPr_def_18)
| member(X0,iPr_def_17)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2653,c_165]) ).
tcf(c_3830,plain,
! [X0: $i] :
( member(X0,iPr_def_21)
| member(X0,iPr_def_20)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2656,c_165]) ).
tcf(c_3832,plain,
! [X0: $i] :
( member(X0,iPr_def_24)
| member(X0,iPr_def_23)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2659,c_165]) ).
tcf(c_7002,plain,
( member(u,iPr_def_18)
| member(u,iPr_def_17) ),
inference(superposition,[status(thm)],[c_2661,c_3828]) ).
tcf(c_7743,plain,
( member(u,iPr_def_21)
| member(u,iPr_def_20) ),
inference(superposition,[status(thm)],[c_2661,c_3830]) ).
tcf(c_8871,plain,
( member(u,iPr_def_24)
| member(u,iPr_def_23) ),
inference(superposition,[status(thm)],[c_2661,c_3832]) ).
tcf(c_8896,plain,
member(u,iPr_def_23),
inference(forward_subsumption_resolution,[status(thm)],[c_8871,c_2660]) ).
tcf(c_8959,plain,
member(u,iPr_def_22),
inference(superposition,[status(thm)],[c_8896,c_3575]) ).
tcf(c_8989,plain,
~ member(u,iPr_def_21),
inference(superposition,[status(thm)],[c_8959,c_3612]) ).
tcf(c_8993,plain,
member(u,iPr_def_20),
inference(backward_subsumption_resolution,[status(thm)],[c_7743,c_8989]) ).
tcf(c_9019,plain,
member(u,iPr_def_19),
inference(superposition,[status(thm)],[c_8993,c_3574]) ).
tcf(c_9024,plain,
~ member(u,iPr_def_18),
inference(superposition,[status(thm)],[c_9019,c_3610]) ).
tcf(c_9028,plain,
member(u,iPr_def_17),
inference(backward_subsumption_resolution,[status(thm)],[c_7002,c_9024]) ).
tcf(c_9034,plain,
member(u,iPr_def_15),
inference(superposition,[status(thm)],[c_9028,c_3536]) ).
tcf(c_9048,plain,
~ member(u,iPr_def_14),
inference(superposition,[status(thm)],[c_9034,c_3608]) ).
tcf(c_9049,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9048,c_3511]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET132-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/5.40 % Computer : n013.cluster.edu
% 0.02/5.40 % Model : x86_64 x86_64
% 0.02/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/5.40 % Memory : 8046.5625MB
% 0.02/5.40 % OS : Linux 6.8.0-71-generic
% 0.02/5.40 % CPULimit : 300
% 0.02/5.40 % WCLimit : 300
% 0.02/5.40 % DateTime : Thu Sep 24 09:58:21 UTC 2026
% 0.02/5.40 % CPUTime :
% 0.02/5.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/5.44 Running first-order theorem proving
% 0.02/5.44 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
% 0.02/5.45
% 0.02/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.02/5.45
% 0.02/5.45 % Detected problem language: tptp
% 0.02/5.46 % Proving...
% 4.84/6.77 % SZS status Started for theBenchmark.p
% 4.84/6.77 % SZS status Unsatisfiable for theBenchmark.p
% 4.84/6.77
% 4.84/6.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.84/6.77
% 4.84/6.77 % ------ iProver source info
% 4.84/6.77
% 4.84/6.77 % git: date: 2026-07-19 20:42:38 +0200
% 4.84/6.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.84/6.77 % git: non_committed_changes: false
% 4.84/6.77
% 4.84/6.77 % ------ Parsing...% successful
% 4.84/6.77
% 4.84/6.77
% 4.84/6.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.84/6.77
% 4.84/6.77 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.84/6.77
% 4.84/6.77 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.84/6.77
% 4.84/6.77 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.84/6.77 % ------ Proving...
% 4.84/6.77 % ------ Problem Properties
% 4.84/6.77
% 4.84/6.77 %
% 4.84/6.77 % clauses 84
% 4.84/6.77 % conjectures 2
% 4.84/6.77 % EPR 14
% 4.84/6.77 % Horn 76
% 4.84/6.77 % unary 32
% 4.84/6.77 % binary 32
% 4.84/6.77 % lits 162
% 4.84/6.77 % lits eq 35
% 4.84/6.77 % fd_pure 0
% 4.84/6.77 % fd_pseudo 0
% 4.84/6.77 % fd_cond 3
% 4.84/6.77 % fd_pseudo_cond 3
% 4.84/6.77 % AC symbols 0
% 4.84/6.77
% 4.84/6.77 % ------ Schedule dynamic 5 is on
% 4.84/6.77
% 4.84/6.77 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.84/6.77
% 4.84/6.77
% 4.84/6.77 % ------
% 4.84/6.77 % Current options:
% 4.84/6.77 % ------
% 4.84/6.77
% 4.84/6.77
% 4.84/6.77 %
% 4.84/6.77
% 4.84/6.77 % ------ Proving...
% 4.84/6.77 %
% 4.84/6.77
% 4.84/6.77 % SZS status Unsatisfiable for theBenchmark.p
% 4.84/6.77
% 4.84/6.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.84/6.77
% 4.84/6.77
%------------------------------------------------------------------------------