%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET085-7 : 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 : n010.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 02:46:31 PM UTC 2026
% Result : Unsatisfiable 3.62s 1.18s
% Output : CNFRefutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 30 unt; 2 def)
% Number of atoms : 89 ( 37 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?; 13 :)
% 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(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f113,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f123,axiom,
! [X0,X1] :
( unordered_pair(X1,X0) = singleton(X1)
| member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
fof(f137,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f138,axiom,
! [X0] :
( singleton(X0) = null_class
| member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f141,negated_conjecture,
unordered_pair(y,z) = singleton(x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_1) ).
fof(f142,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_2) ).
fof(f143,negated_conjecture,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_3) ).
fof(f144,plain,
y != x,
inference(reorient_equations,[],[f143]) ).
fof(f145,negated_conjecture,
x != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_4) ).
fof(f146,plain,
z != x,
inference(reorient_equations,[],[f145]) ).
fof(f201,plain,
! [X0,X1] :
( unordered_pair(X1,X0) = unordered_pair(X1,X1)
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f123,f12]) ).
fof(f211,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f137,f12]) ).
fof(f212,plain,
! [X0] :
( unordered_pair(X0,X0) = null_class
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f138,f12]) ).
fof(f215,plain,
unordered_pair(y,z) = unordered_pair(x,x),
inference(definition_unfolding,[],[f141,f12]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_267,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f113]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ( unordered_pair(X0,X0) = unordered_pair(X0,X1) ) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_290,plain,
! [X0: $i] :
( member(X0,universal_class)
| ( unordered_pair(X0,X0) = null_class ) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_293,negated_conjecture,
unordered_pair(y,z) = unordered_pair(x,x),
inference(cnf_transformation,[],[f215]) ).
tcf(c_294,negated_conjecture,
member(x,universal_class),
inference(cnf_transformation,[],[f142]) ).
tcf(c_295,negated_conjecture,
y != x,
inference(cnf_transformation,[],[f144]) ).
tcf(c_296,negated_conjecture,
z != x,
inference(cnf_transformation,[],[f146]) ).
tcf(c_3327,definition,
iPr_def_10 = unordered_pair(y,z),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3328,definition,
iPr_def_11 = unordered_pair(x,x),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3329,negated_conjecture,
z != x,
inference(demodulation,[status(thm)],[c_296]) ).
tcf(c_3330,negated_conjecture,
y != x,
inference(demodulation,[status(thm)],[c_295]) ).
tcf(c_3331,negated_conjecture,
member(x,universal_class),
inference(demodulation,[status(thm)],[c_294]) ).
tcf(c_3332,negated_conjecture,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_293,c_3328,c_3327]) ).
tcf(c_4365,plain,
unordered_pair(x,x) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_3328,c_3332]) ).
tcf(c_4443,plain,
( member(y,iPr_def_10)
| ~ member(y,universal_class) ),
inference(superposition,[status(thm)],[c_3327,c_189]) ).
tcf(c_4444,plain,
( member(x,iPr_def_10)
| ~ member(x,universal_class) ),
inference(superposition,[status(thm)],[c_4365,c_189]) ).
tcf(c_4445,plain,
member(x,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_4444,c_3331]) ).
tcf(c_4454,plain,
( member(z,iPr_def_10)
| ~ member(z,universal_class) ),
inference(superposition,[status(thm)],[c_3327,c_190]) ).
tcf(c_4557,plain,
( member(y,iPr_def_10)
| ( unordered_pair(y,y) = null_class ) ),
inference(superposition,[status(thm)],[c_290,c_4443]) ).
tcf(c_4558,plain,
( member(z,iPr_def_10)
| ( unordered_pair(z,z) = null_class ) ),
inference(superposition,[status(thm)],[c_290,c_4454]) ).
tcf(c_4597,plain,
! [X0: $i] :
( ( X0 = x )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4365,c_289]) ).
tcf(c_4735,plain,
( ( y = x )
| ( unordered_pair(y,y) = null_class ) ),
inference(superposition,[status(thm)],[c_4557,c_4597]) ).
tcf(c_4737,plain,
( ( z = x )
| ( unordered_pair(z,z) = null_class ) ),
inference(superposition,[status(thm)],[c_4558,c_4597]) ).
tcf(c_4742,plain,
unordered_pair(z,z) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[c_4737,c_3329]) ).
tcf(c_4743,plain,
unordered_pair(y,y) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[c_4735,c_3330]) ).
tcf(c_4752,plain,
( member(z,null_class)
| ~ member(z,universal_class) ),
inference(superposition,[status(thm)],[c_4742,c_190]) ).
tcf(c_4759,plain,
~ member(z,universal_class),
inference(forward_subsumption_resolution,[status(thm)],[c_4752,c_267]) ).
tcf(c_4894,plain,
! [X0: $i] : unordered_pair(X0,X0) = unordered_pair(X0,z),
inference(superposition,[status(thm)],[c_275,c_4759]) ).
tcf(c_4896,plain,
unordered_pair(y,y) = iPr_def_10,
inference(demodulation,[status(thm)],[c_3327,c_4894]) ).
tcf(c_4897,plain,
null_class = iPr_def_10,
inference(demodulation,[status(thm)],[c_4743,c_4896]) ).
tcf(c_4908,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_267,c_4897]) ).
tcf(c_4911,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_4445,c_4908]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET085-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 09:41:28 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 0.15/0.41
% 0.15/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.41
% 0.15/0.42 % Detected problem language: tptp
% 0.15/0.42 % Proving...
% 3.62/1.18 % SZS status Started for theBenchmark.p
% 3.62/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.62/1.18
% 3.62/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.62/1.18
% 3.62/1.18 % ------ iProver source info
% 3.62/1.18
% 3.62/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.62/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.62/1.18 % git: non_committed_changes: false
% 3.62/1.18
% 3.62/1.18 % ------ Parsing...% successful
% 3.62/1.18
% 3.62/1.18
% 3.62/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.62/1.18
% 3.62/1.18 % ------ 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 %
% 3.62/1.18
% 3.62/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.62/1.18
% 3.62/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.62/1.18 % ------ Proving...
% 3.62/1.18 % ------ Problem Properties
% 3.62/1.18
% 3.62/1.18 %
% 3.62/1.18 % clauses 105
% 3.62/1.18 % conjectures 4
% 3.62/1.18 % EPR 21
% 3.62/1.18 % Horn 90
% 3.62/1.18 % unary 30
% 3.62/1.18 % binary 45
% 3.62/1.18 % lits 216
% 3.62/1.18 % lits eq 47
% 3.62/1.18 % fd_pure 0
% 3.62/1.18 % fd_pseudo 0
% 3.62/1.18 % fd_cond 5
% 3.62/1.18 % fd_pseudo_cond 11
% 3.62/1.18 % AC symbols 0
% 3.62/1.18
% 3.62/1.18 % ------ Schedule dynamic 5 is on
% 3.62/1.18
% 3.62/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.62/1.18
% 3.62/1.18
% 3.62/1.18 % ------
% 3.62/1.18 % Current options:
% 3.62/1.18 % ------
% 3.62/1.18
% 3.62/1.18
% 3.62/1.18 %
% 3.62/1.18
% 3.62/1.18 % ------ Proving...
% 3.62/1.18 %
% 3.62/1.18
% 3.62/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.62/1.18
% 3.62/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.62/1.18
% 3.62/1.18
%------------------------------------------------------------------------------