%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN015-2 : 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 : n009.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 03:38:53 PM UTC 2026
% Result : Unsatisfiable 0.60s 1.29s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 59 ( 10 unt; 0 def)
% Number of atoms : 170 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 192 ( 81 ~; 111 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : equalish(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivityish) ).
fof(f2,axiom,
! [X0,X1] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetryish) ).
fof(f3,axiom,
! [X2,X0,X1] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivityish) ).
fof(f4,axiom,
! [X2,X0,X1] :
( element(X2,X1)
| ~ element(X2,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_substitutionish1) ).
fof(f5,axiom,
! [X2,X0,X1] :
( element(X2,X1)
| ~ equalish(X0,X2)
| ~ element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_substitutionish2) ).
fof(f8,negated_conjecture,
! [X0] :
( equalish(X0,m)
| ~ element(X0,m)
| ~ equalish(f(X0),m) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_5) ).
fof(f9,negated_conjecture,
! [X0] :
( equalish(X0,m)
| ~ element(X0,m)
| ~ equalish(f(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_6) ).
fof(f10,negated_conjecture,
! [X0] :
( equalish(X0,m)
| ~ element(X0,m)
| element(X0,f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_7) ).
fof(f11,negated_conjecture,
! [X0] :
( equalish(X0,m)
| ~ element(X0,m)
| element(f(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_8) ).
fof(f12,negated_conjecture,
! [X0,X1] :
( equalish(X1,m)
| element(X1,m)
| equalish(X0,m)
| equalish(X0,X1)
| ~ element(X1,X0)
| ~ element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_9) ).
fof(f19,negated_conjecture,
! [X0] :
( equalish(X0,k)
| element(X0,k)
| ~ equalish(X0,n) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_16) ).
fof(f20,negated_conjecture,
! [X0] :
( equalish(X0,k)
| equalish(X0,m)
| equalish(X0,n)
| ~ element(X0,k) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_17) ).
fof(f22,negated_conjecture,
~ equalish(m,n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_19) ).
fof(f23,negated_conjecture,
~ equalish(n,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_20) ).
fof(f26,negated_conjecture,
equalish(m,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_23) ).
tcf(c_75,plain,
! [X0: $i] : equalish(X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ element(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X1,X2)
| ~ element(X0,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_82,negated_conjecture,
! [X0: $i] :
( equalish(X0,m)
| ~ element(X0,m)
| ~ equalish(f(X0),m) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_83,negated_conjecture,
! [X0: $i] :
( equalish(X0,m)
| ~ element(X0,m)
| ~ equalish(f(X0),X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_84,negated_conjecture,
! [X0: $i] :
( equalish(X0,m)
| element(X0,f(X0))
| ~ element(X0,m) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_85,negated_conjecture,
! [X0: $i] :
( equalish(X0,m)
| element(f(X0),X0)
| ~ element(X0,m) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_86,negated_conjecture,
! [X0: $i,X1: $i] :
( element(X1,m)
| equalish(X1,m)
| equalish(X0,m)
| equalish(X0,X1)
| ~ element(X1,X0)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_93,negated_conjecture,
! [X0: $i] :
( element(X0,k)
| equalish(X0,k)
| ~ equalish(X0,n) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_94,negated_conjecture,
! [X0: $i] :
( equalish(X0,n)
| equalish(X0,m)
| equalish(X0,k)
| ~ element(X0,k) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_96,negated_conjecture,
~ equalish(m,n),
inference(cnf_transformation,[],[f22]) ).
tcf(c_97,negated_conjecture,
~ equalish(n,k),
inference(cnf_transformation,[],[f23]) ).
tcf(c_100,negated_conjecture,
equalish(m,k),
inference(cnf_transformation,[],[f26]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] :
( element(X1,m)
| equalish(X1,m)
| equalish(X0,X1)
| ~ element(X1,X0)
| ~ element(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_86,c_78]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i] :
( element(X1,m)
| equalish(X1,m)
| equalish(X0,X1)
| ~ element(X1,X0)
| ~ element(X0,X1) ),
inference(demodulation,[status(thm)],[c_171]) ).
tcf(c_253,negated_conjecture,
! [X0: $i] :
( equalish(X0,n)
| equalish(X0,m)
| equalish(X0,k)
| ~ element(X0,k) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_254,negated_conjecture,
! [X0: $i] :
( element(X0,k)
| equalish(X0,k)
| ~ equalish(X0,n) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_261,negated_conjecture,
! [X0: $i] :
( equalish(X0,m)
| element(f(X0),X0)
| ~ element(X0,m) ),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_262,negated_conjecture,
! [X0: $i] :
( equalish(X0,m)
| element(X0,f(X0))
| ~ element(X0,m) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_263,negated_conjecture,
! [X0: $i] :
( equalish(X0,m)
| ~ element(X0,m)
| ~ equalish(f(X0),X0) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_264,negated_conjecture,
! [X0: $i] :
( equalish(X0,m)
| ~ element(X0,m)
| ~ equalish(f(X0),m) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_267,plain,
( element(n,k)
| equalish(n,k)
| ~ equalish(n,n) ),
inference(instantiation,[status(thm)],[c_254]) ).
tcf(c_277,plain,
( equalish(m,n)
| ~ equalish(n,m) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_296,plain,
equalish(n,n),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_303,plain,
( equalish(n,m)
| ~ element(n,m)
| ~ equalish(f(n),n) ),
inference(instantiation,[status(thm)],[c_263]) ).
tcf(c_304,plain,
( equalish(n,m)
| element(n,f(n))
| ~ element(n,m) ),
inference(instantiation,[status(thm)],[c_262]) ).
tcf(c_305,plain,
( equalish(n,m)
| element(f(n),n)
| ~ element(n,m) ),
inference(instantiation,[status(thm)],[c_261]) ).
tcf(c_306,plain,
( equalish(n,m)
| ~ element(n,m)
| ~ equalish(f(n),m) ),
inference(instantiation,[status(thm)],[c_264]) ).
tcf(c_309,plain,
! [X0: $i] :
( element(n,X0)
| ~ element(n,k)
| ~ equalish(k,X0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_310,plain,
( element(n,m)
| ~ element(n,k)
| ~ equalish(k,m) ),
inference(instantiation,[status(thm)],[c_309]) ).
tcf(c_311,plain,
! [X0: $i] :
( element(X0,k)
| ~ element(n,k)
| ~ equalish(n,X0) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_466,plain,
! [X0: $i] :
( equalish(k,X0)
| ~ equalish(X0,k) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_467,plain,
( equalish(k,m)
| ~ equalish(m,k) ),
inference(instantiation,[status(thm)],[c_466]) ).
tcf(c_640,plain,
! [X0: $i] :
( equalish(f(n),m)
| ~ equalish(X0,m)
| ~ equalish(f(n),X0) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_645,plain,
! [X0: $i] :
( element(f(n),m)
| equalish(f(n),m)
| equalish(X0,f(n))
| ~ element(X0,f(n))
| ~ element(f(n),X0) ),
inference(instantiation,[status(thm)],[c_246]) ).
tcf(c_785,plain,
( equalish(f(n),m)
| ~ equalish(k,m)
| ~ equalish(f(n),k) ),
inference(instantiation,[status(thm)],[c_640]) ).
tcf(c_786,plain,
( equalish(f(n),n)
| equalish(f(n),m)
| equalish(f(n),k)
| ~ element(f(n),k) ),
inference(instantiation,[status(thm)],[c_253]) ).
tcf(c_846,plain,
( element(f(n),m)
| equalish(n,f(n))
| equalish(f(n),m)
| ~ element(n,f(n))
| ~ element(f(n),n) ),
inference(instantiation,[status(thm)],[c_645]) ).
tcf(c_969,plain,
! [X0: $i] :
( element(f(n),X0)
| ~ equalish(m,X0)
| ~ element(f(n),m) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_1425,plain,
( element(f(n),k)
| ~ element(n,k)
| ~ equalish(n,f(n)) ),
inference(instantiation,[status(thm)],[c_311]) ).
tcf(c_1658,plain,
( element(f(n),k)
| ~ equalish(m,k)
| ~ element(f(n),m) ),
inference(instantiation,[status(thm)],[c_969]) ).
tcf(c_1659,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1658,c_1425,c_846,c_786,c_785,c_467,c_310,c_303,c_304,c_305,c_306,c_296,c_277,c_267,c_96,c_97,c_100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN015-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 23:51:29 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 0.60/1.29 % SZS status Started for theBenchmark.p
% 0.60/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.60/1.29
% 0.60/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.60/1.29
% 0.60/1.29 % ------ iProver source info
% 0.60/1.29
% 0.60/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.60/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.60/1.29 % git: non_committed_changes: false
% 0.60/1.29
% 0.60/1.29 % ------ Parsing...% successful
% 0.60/1.29
% 0.60/1.29
% 0.60/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.60/1.29
% 0.60/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.60/1.29
% 0.60/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.60/1.29 % ------ Proving...
% 0.60/1.29 % ------ Problem Properties
% 0.60/1.29
% 0.60/1.29 %
% 0.60/1.29 % clauses 26
% 0.60/1.29 % conjectures 20
% 0.60/1.29 % EPR 18
% 0.60/1.29 % Horn 13
% 0.60/1.29 % unary 7
% 0.60/1.29 % binary 1
% 0.60/1.29 % lits 69
% 0.60/1.29 % lits eq 0
% 0.60/1.29 % fd_pure 0
% 0.60/1.29 % fd_pseudo 0
% 0.60/1.29 % fd_cond 0
% 0.60/1.29 % fd_pseudo_cond 0
% 0.60/1.29 % AC symbols 0
% 0.60/1.29
% 0.60/1.29 % ------ Schedule dynamic 5 is on
% 0.60/1.29
% 0.60/1.29 % ------ no equalities: superposition off
% 0.60/1.29
% 0.60/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.60/1.29
% 0.60/1.29
% 0.60/1.29 % ------
% 0.60/1.29 % Current options:
% 0.60/1.29 % ------
% 0.60/1.29
% 0.60/1.29
% 0.60/1.29 %
% 0.60/1.29
% 0.60/1.29 % ------ Proving...
% 0.60/1.29 %
% 0.60/1.29
% 0.60/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.60/1.29
% 0.60/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.60/1.29
% 0.60/1.29
%------------------------------------------------------------------------------