%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 02:46:05 PM UTC 2026
% Result : Unsatisfiable 3.39s 1.52s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 26 unt; 0 def)
% Number of atoms : 64 ( 42 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 9 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : member(X0,singleton_set(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_1) ).
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_2) ).
fof(f3,axiom,
! [X0,X1] : member(X0,unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_1) ).
fof(f4,axiom,
! [X0,X1] : member(X0,unordered_pair(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_2) ).
fof(f5,axiom,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_3) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton_set(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f7,axiom,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_ordered_pairs) ).
fof(f8,negated_conjecture,
r1 != r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_second_components_equal) ).
fof(f9,plain,
unordered_pair(singleton_set(m1),unordered_pair(m1,r1)) = unordered_pair(singleton_set(m2),unordered_pair(m2,r2)),
inference(definition_unfolding,[],[f7,f6,f6]) ).
tcf(c_57,plain,
! [X0: $i] : member(X0,singleton_set(X0)),
inference(cnf_transformation,[],[f1]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X0,singleton_set(X1)) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : member(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : member(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_62,plain,
unordered_pair(singleton_set(m1),unordered_pair(m1,r1)) = unordered_pair(singleton_set(m2),unordered_pair(m2,r2)),
inference(cnf_transformation,[],[f9]) ).
tcf(c_63,negated_conjecture,
r1 != r2,
inference(cnf_transformation,[],[f8]) ).
tcf(c_177,negated_conjecture,
r1 != r2,
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_289,plain,
member(singleton_set(m2),unordered_pair(singleton_set(m1),unordered_pair(m1,r1))),
inference(superposition,[status(thm)],[c_62,c_59]) ).
tcf(c_290,plain,
member(unordered_pair(m2,r2),unordered_pair(singleton_set(m1),unordered_pair(m1,r1))),
inference(superposition,[status(thm)],[c_62,c_60]) ).
tcf(c_296,plain,
( ( singleton_set(m1) = singleton_set(m2) )
| ( unordered_pair(m1,r1) = singleton_set(m2) ) ),
inference(superposition,[status(thm)],[c_289,c_61]) ).
tcf(c_303,plain,
( member(m1,singleton_set(m2))
| ( singleton_set(m1) = singleton_set(m2) ) ),
inference(superposition,[status(thm)],[c_296,c_59]) ).
tcf(c_325,plain,
( ( m1 = m2 )
| ( singleton_set(m1) = singleton_set(m2) ) ),
inference(superposition,[status(thm)],[c_303,c_58]) ).
tcf(c_339,plain,
( member(m2,singleton_set(m1))
| ( m1 = m2 ) ),
inference(superposition,[status(thm)],[c_325,c_57]) ).
tcf(c_353,plain,
( ( r1 = r2 )
| ~ member(r1,singleton_set(r2)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_358,plain,
m1 = m2,
inference(superposition,[status(thm)],[c_339,c_58]) ).
tcf(c_361,plain,
member(unordered_pair(m1,r2),unordered_pair(singleton_set(m1),unordered_pair(m1,r1))),
inference(demodulation,[status(thm)],[c_290,c_358]) ).
tcf(c_364,plain,
unordered_pair(singleton_set(m1),unordered_pair(m1,r1)) = unordered_pair(singleton_set(m1),unordered_pair(m1,r2)),
inference(demodulation,[status(thm)],[c_62,c_358]) ).
tcf(c_366,plain,
( ( unordered_pair(m1,r2) = singleton_set(m1) )
| ( unordered_pair(m1,r1) = unordered_pair(m1,r2) ) ),
inference(superposition,[status(thm)],[c_361,c_61]) ).
tcf(c_389,plain,
( member(r2,unordered_pair(m1,r1))
| ( unordered_pair(m1,r2) = singleton_set(m1) ) ),
inference(superposition,[status(thm)],[c_366,c_60]) ).
tcf(c_403,plain,
( ( r1 = r2 )
| ( m1 = r2 )
| ( unordered_pair(m1,r2) = singleton_set(m1) ) ),
inference(superposition,[status(thm)],[c_389,c_61]) ).
tcf(c_404,plain,
( ( m1 = r2 )
| ( unordered_pair(m1,r2) = singleton_set(m1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_403,c_177]) ).
tcf(c_413,plain,
( member(r2,singleton_set(m1))
| ( m1 = r2 ) ),
inference(superposition,[status(thm)],[c_404,c_60]) ).
tcf(c_431,plain,
m1 = r2,
inference(superposition,[status(thm)],[c_413,c_58]) ).
tcf(c_433,plain,
( ( unordered_pair(r2,r2) = singleton_set(r2) )
| ( unordered_pair(r2,r1) = unordered_pair(r2,r2) ) ),
inference(demodulation,[status(thm)],[c_366,c_431]) ).
tcf(c_434,plain,
unordered_pair(singleton_set(r2),unordered_pair(r2,r1)) = unordered_pair(singleton_set(r2),unordered_pair(r2,r2)),
inference(demodulation,[status(thm)],[c_364,c_431]) ).
tcf(c_457,plain,
! [X0: $i] :
( ( X0 = r2 )
| ( unordered_pair(r2,r2) = singleton_set(r2) )
| ~ member(X0,unordered_pair(r2,r1)) ),
inference(superposition,[status(thm)],[c_433,c_61]) ).
tcf(c_474,plain,
( ( r1 = r2 )
| ( unordered_pair(r2,r2) = singleton_set(r2) ) ),
inference(superposition,[status(thm)],[c_60,c_457]) ).
tcf(c_475,plain,
unordered_pair(r2,r2) = singleton_set(r2),
inference(forward_subsumption_resolution,[status(thm)],[c_474,c_177]) ).
tcf(c_476,plain,
unordered_pair(singleton_set(r2),unordered_pair(r2,r1)) = unordered_pair(singleton_set(r2),singleton_set(r2)),
inference(demodulation,[status(thm)],[c_434,c_475]) ).
tcf(c_484,plain,
member(unordered_pair(r2,r1),unordered_pair(singleton_set(r2),singleton_set(r2))),
inference(superposition,[status(thm)],[c_476,c_60]) ).
tcf(c_490,plain,
unordered_pair(r2,r1) = singleton_set(r2),
inference(superposition,[status(thm)],[c_484,c_61]) ).
tcf(c_503,plain,
member(r1,singleton_set(r2)),
inference(superposition,[status(thm)],[c_490,c_60]) ).
tcf(c_508,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_503,c_353,c_63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.45 % Computer : n002.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Thu Sep 24 09:14:04 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.26/0.50 Running first-order theorem proving
% 0.26/0.51 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
% 0.26/0.52
% 0.26/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.52
% 0.26/0.52 % Detected problem language: tptp
% 0.26/0.54 % Proving...
% 3.39/1.52 % SZS status Started for theBenchmark.p
% 3.39/1.52 % SZS status Unsatisfiable for theBenchmark.p
% 3.39/1.52
% 3.39/1.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.39/1.52
% 3.39/1.52 % ------ iProver source info
% 3.39/1.52
% 3.39/1.52 % git: date: 2026-07-19 20:42:38 +0200
% 3.39/1.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.39/1.52 % git: non_committed_changes: false
% 3.39/1.52
% 3.39/1.52 % ------ Parsing...% successful
% 3.39/1.52
% 3.39/1.52
% 3.39/1.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.39/1.52
% 3.39/1.52 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.39/1.52
% 3.39/1.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.39/1.52
% 3.39/1.52 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.39/1.52 % ------ Proving...
% 3.39/1.52 % ------ Problem Properties
% 3.39/1.52
% 3.39/1.52 %
% 3.39/1.52 % clauses 7
% 3.39/1.52 % conjectures 1
% 3.39/1.52 % EPR 1
% 3.39/1.52 % Horn 6
% 3.39/1.52 % unary 5
% 3.39/1.52 % binary 1
% 3.39/1.52 % lits 10
% 3.39/1.52 % lits eq 5
% 3.39/1.52 % fd_pure 0
% 3.39/1.52 % fd_pseudo 0
% 3.39/1.52 % fd_cond 0
% 3.39/1.52 % fd_pseudo_cond 2
% 3.39/1.52 % AC symbols 0
% 3.39/1.52
% 3.39/1.52 % ------ Schedule dynamic 5 is on
% 3.39/1.52
% 3.39/1.52 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.39/1.52
% 3.39/1.52
% 3.39/1.52 % ------
% 3.39/1.52 % Current options:
% 3.39/1.52 % ------
% 3.39/1.52
% 3.39/1.52
% 3.39/1.52 %
% 3.39/1.52
% 3.39/1.52 % ------ Proving...
% 3.39/1.52 %
% 3.39/1.52
% 3.39/1.52 % SZS status Unsatisfiable for theBenchmark.p
% 3.39/1.52
% 3.39/1.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.39/1.52
% 3.39/1.52
%------------------------------------------------------------------------------