%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MSC012+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n018.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 02:13:58 PM UTC 2026
% Result : Theorem 1.68s 1.28s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 13 unt; 0 def)
% Number of atoms : 161 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 137 ( 64 ~; 66 |; 5 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-1 aty)
% Number of variables : 58 ( 0 sgn 56 !; 2 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( p(X1)
& less(X0,X1)
& p(X0) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_to_right) ).
fof(f2,axiom,
! [X0] :
( ? [X1] :
( p(X1)
& less(X0,X1) )
| p(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_to_left) ).
fof(f3,axiom,
! [X0,X1,X2] :
( ( less(X1,X2)
& less(X0,X1) )
=> less(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_less) ).
fof(f4,axiom,
! [X0] :
? [X1] : less(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',serial_less) ).
fof(f5,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(f6,negated_conjecture,
~ goal,
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
~ goal,
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ~ p(X1)
| ~ less(X0,X1)
| ~ p(X0)
| goal ),
inference(ennf_transformation,[],[f1]) ).
fof(f9,plain,
! [X0,X1] :
( ~ p(X1)
| ~ less(X0,X1)
| ~ p(X0)
| goal ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ~ less(X1,X2)
| ~ less(X0,X1)
| less(X0,X2) ),
inference(ennf_transformation,[],[f3]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ~ less(X1,X2)
| ~ less(X0,X1)
| less(X0,X2) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0] :
( ( p(sK0(X0))
& less(X0,sK0(X0)) )
| p(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f2]) ).
fof(f13,plain,
! [X0] : less(X0,sK1(X0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f4]) ).
fof(f14,plain,
! [X0,X1] :
( ~ p(X1)
| ~ less(X0,X1)
| ~ p(X0)
| goal ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
! [X0] :
( p(sK0(X0))
| p(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f16,plain,
! [X0] :
( less(X0,sK0(X0))
| p(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
! [X2,X0,X1] :
( ~ less(X1,X2)
| ~ less(X0,X1)
| less(X0,X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0] : less(X0,sK1(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
~ goal,
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( goal
| ~ p(X1)
| ~ p(X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_50,plain,
! [X0: $i] :
( p(X0)
| less(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_51,plain,
! [X0: $i] :
( p(X0)
| p(sK0(X0)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_53,plain,
! [X0: $i] : less(X0,sK1(X0)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_54,negated_conjecture,
~ goal,
inference(cnf_transformation,[],[f19]) ).
tcf(c_55,plain,
less(iProver_bot,sK1(iProver_bot)),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_56,plain,
( p(iProver_bot)
| p(sK0(iProver_bot)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ~ less(X0,X1)
| ~ p(X0)
| ~ p(X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_54,c_49]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ~ p(X1)
| ~ p(X0)
| ~ less(X0,X1) ),
inference(renaming,[status(thm)],[c_59]) ).
tcf(c_108,plain,
! [X0: $i] :
( ~ p(X0)
| ~ p(sK1(X0))
| ~ less(X0,sK1(X0)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_109,plain,
( ~ p(iProver_bot)
| ~ p(sK1(iProver_bot))
| ~ less(iProver_bot,sK1(iProver_bot)) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( less(X0,X1)
| ~ less(X0,sK1(X0))
| ~ less(sK1(X0),X1) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_112,plain,
! [X0: $i] :
( p(sK1(X0))
| less(sK1(X0),sK0(sK1(X0))) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_113,plain,
! [X0: $i] :
( p(sK1(X0))
| p(sK0(sK1(X0))) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_114,plain,
( p(sK1(iProver_bot))
| p(sK0(sK1(iProver_bot))) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_127,plain,
! [X0: $i] :
( less(X0,sK0(sK1(X0)))
| ~ less(X0,sK1(X0))
| ~ less(sK1(X0),sK0(sK1(X0))) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_143,plain,
! [X0: $i] :
( ~ p(sK0(X0))
| ~ p(sK1(sK0(X0)))
| ~ less(sK0(X0),sK1(sK0(X0))) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_144,plain,
( ~ p(sK0(iProver_bot))
| ~ p(sK1(sK0(iProver_bot)))
| ~ less(sK0(iProver_bot),sK1(sK0(iProver_bot))) ),
inference(instantiation,[status(thm)],[c_143]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] :
( less(X0,X1)
| ~ less(sK1(X0),X1) ),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_260,plain,
! [X0: $i] : less(sK0(X0),sK1(sK0(X0))),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_262,plain,
less(sK0(iProver_bot),sK1(sK0(iProver_bot))),
inference(instantiation,[status(thm)],[c_260]) ).
tcf(c_275,plain,
! [X0: $i] :
( p(sK1(sK0(X0)))
| less(sK1(sK0(X0)),sK0(sK1(sK0(X0)))) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_276,plain,
! [X0: $i] :
( p(sK1(sK0(X0)))
| p(sK0(sK1(sK0(X0)))) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_277,plain,
( p(sK1(sK0(iProver_bot)))
| p(sK0(sK1(sK0(iProver_bot)))) ),
inference(instantiation,[status(thm)],[c_276]) ).
tcf(c_278,plain,
( p(sK1(sK0(iProver_bot)))
| less(sK1(sK0(iProver_bot)),sK0(sK1(sK0(iProver_bot)))) ),
inference(instantiation,[status(thm)],[c_275]) ).
tcf(c_283,plain,
! [X0: $i] :
( p(sK1(X0))
| less(X0,sK0(sK1(X0))) ),
inference(superposition,[status(thm)],[c_50,c_212]) ).
tcf(c_437,plain,
! [X0: $i] :
( p(sK1(X0))
| ~ p(X0)
| ~ p(sK0(sK1(X0))) ),
inference(superposition,[status(thm)],[c_283,c_60]) ).
tcf(c_448,plain,
( p(sK1(iProver_bot))
| ~ p(iProver_bot)
| ~ p(sK0(sK1(iProver_bot))) ),
inference(instantiation,[status(thm)],[c_437]) ).
tcf(c_479,plain,
! [X0: $i] :
( ~ p(X0)
| ~ p(sK0(sK1(X0)))
| ~ less(X0,sK0(sK1(X0))) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_491,plain,
! [X0: $i] :
( less(sK0(X0),sK0(sK1(sK0(X0))))
| ~ less(sK0(X0),sK1(sK0(X0)))
| ~ less(sK1(sK0(X0)),sK0(sK1(sK0(X0)))) ),
inference(instantiation,[status(thm)],[c_127]) ).
tcf(c_493,plain,
( less(sK0(iProver_bot),sK0(sK1(sK0(iProver_bot))))
| ~ less(sK0(iProver_bot),sK1(sK0(iProver_bot)))
| ~ less(sK1(sK0(iProver_bot)),sK0(sK1(sK0(iProver_bot)))) ),
inference(instantiation,[status(thm)],[c_491]) ).
tcf(c_734,plain,
! [X0: $i] :
( ~ p(sK0(X0))
| ~ p(sK0(sK1(sK0(X0))))
| ~ less(sK0(X0),sK0(sK1(sK0(X0)))) ),
inference(instantiation,[status(thm)],[c_479]) ).
tcf(c_735,plain,
( ~ p(sK0(iProver_bot))
| ~ p(sK0(sK1(sK0(iProver_bot))))
| ~ less(sK0(iProver_bot),sK0(sK1(sK0(iProver_bot)))) ),
inference(instantiation,[status(thm)],[c_734]) ).
tcf(c_827,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_735,c_493,c_448,c_278,c_277,c_262,c_144,c_114,c_109,c_56,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MSC012+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 01:30:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.68/1.28 % SZS status Started for theBenchmark.p
% 1.68/1.28 % SZS status Theorem for theBenchmark.p
% 1.68/1.28
% 1.68/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.68/1.28
% 1.68/1.28 % ------ iProver source info
% 1.68/1.28
% 1.68/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.68/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.68/1.28 % git: non_committed_changes: false
% 1.68/1.28
% 1.68/1.28 % ------ Parsing...
% 1.68/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.68/1.28
% 1.68/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.68/1.28
% 1.68/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.68/1.28 % ------ Proving...
% 1.68/1.28 % ------ Problem Properties
% 1.68/1.28
% 1.68/1.28 %
% 1.68/1.28 % clauses 5
% 1.68/1.28 % conjectures 0
% 1.68/1.28 % EPR 2
% 1.68/1.28 % Horn 3
% 1.68/1.28 % unary 1
% 1.68/1.28 % binary 2
% 1.68/1.28 % lits 11
% 1.68/1.28 % lits eq 0
% 1.68/1.28 % fd_pure 0
% 1.68/1.28 % fd_pseudo 0
% 1.68/1.28 % fd_cond 0
% 1.68/1.28 % fd_pseudo_cond 0
% 1.68/1.28 % AC symbols 0
% 1.68/1.28
% 1.68/1.28 % ------ Schedule dynamic 5 is on
% 1.68/1.28
% 1.68/1.28 % ------ no conjectures: strip conj schedule
% 1.68/1.28
% 1.68/1.28 % ------ no equalities: superposition off
% 1.68/1.28
% 1.68/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.68/1.28
% 1.68/1.28
% 1.68/1.28 % ------
% 1.68/1.28 % Current options:
% 1.68/1.28 % ------
% 1.68/1.28
% 1.68/1.28
% 1.68/1.28 %
% 1.68/1.28
% 1.68/1.28 % ------ Proving...
% 1.68/1.28 %
% 1.68/1.28
% 1.68/1.28 % SZS status Theorem for theBenchmark.p
% 1.68/1.28
% 1.68/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.68/1.28
% 1.68/1.28
%------------------------------------------------------------------------------