%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT031-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:40:38 PM UTC 2026
% Result : Unsatisfiable 8.25s 1.72s
% Output : CNFRefutation 8.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 7 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f145,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_lessequals(c_Set_Oimage(X1,X5,X4,X0),X3,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X5))
| hBOOL(hAPP(hAPP(c_in(X0),hAPP(X1,X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
fof(f382,axiom,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X2,X3)),X0),c_FuncSet_OPi(X1,c_COMBK(X4,tc_fun(X3,tc_bool),X2),X2,X3)))
| c_lessequals(c_Set_Oimage(X0,X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcset__image_0) ).
fof(f746,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f747,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f748,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tcf(c_745,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(cnf_transformation,[],[f748]) ).
tcf(c_751,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(cnf_transformation,[],[f747]) ).
tcf(c_754,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
inference(cnf_transformation,[],[f746]) ).
tcf(c_763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_lessequals(c_Set_Oimage(X2,X3,X0,X1),X4,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X3,c_COMBK(X4,tc_fun(X1,tc_bool),X0),X0,X1))) ),
inference(cnf_transformation,[],[f382]) ).
tcf(c_844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( hBOOL(hAPP(hAPP(c_in(X3),hAPP(X0,X5)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X5),X1))
| ~ c_lessequals(c_Set_Oimage(X0,X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_13066,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(X1),v_Q____),X0))
| ~ c_lessequals(c_Set_Oimage(v_F,X0,X1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) ),
inference(instantiation,[status(thm)],[c_844]) ).
tcf(c_13496,plain,
( c_lessequals(c_Set_Oimage(v_F,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ),
inference(instantiation,[status(thm)],[c_763]) ).
tcf(c_13839,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Q____),c_Arrow__Order__Mirabelle_OProf))
| ~ c_lessequals(c_Set_Oimage(v_F,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool)) ),
inference(instantiation,[status(thm)],[c_13066]) ).
tcf(c_13840,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13839,c_13496,c_754,c_745,c_751]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT031-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 08:37:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 8.25/1.72 % SZS status Started for theBenchmark.p
% 8.25/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 8.25/1.72
% 8.25/1.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.25/1.72
% 8.25/1.72 % ------ iProver source info
% 8.25/1.72
% 8.25/1.72 % git: date: 2026-07-19 20:42:38 +0200
% 8.25/1.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.25/1.72 % git: non_committed_changes: false
% 8.25/1.72
% 8.25/1.72 % ------ Parsing...% successful
% 8.25/1.72
% 8.25/1.72
% 8.25/1.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.25/1.72
% 8.25/1.72 % ------ Preprocessing... sup_sim: 18 sf_s rm: 7 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 8.25/1.72
% 8.25/1.72 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.25/1.72
% 8.25/1.72 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.25/1.72 % ------ Proving...
% 8.25/1.72 % ------ Problem Properties
% 8.25/1.72
% 8.25/1.72 %
% 8.25/1.72 % clauses 205
% 8.25/1.72 % conjectures 1
% 8.25/1.72 % EPR 1
% 8.25/1.72 % Horn 183
% 8.25/1.72 % unary 84
% 8.25/1.72 % binary 78
% 8.25/1.72 % lits 371
% 8.25/1.72 % lits eq 141
% 8.25/1.72 % fd_pure 0
% 8.25/1.72 % fd_pseudo 0
% 8.25/1.72 % fd_cond 0
% 8.25/1.72 % fd_pseudo_cond 22
% 8.25/1.72 % AC symbols 0
% 8.25/1.72
% 8.25/1.72 % ------ Schedule dynamic 5 is on
% 8.25/1.72
% 8.25/1.72 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.25/1.72
% 8.25/1.72
% 8.25/1.72 % ------
% 8.25/1.72 % Current options:
% 8.25/1.72 % ------
% 8.25/1.72
% 8.25/1.72
% 8.25/1.72 %
% 8.25/1.72
% 8.25/1.72 % ------ Proving...
% 8.25/1.72 %
% 8.25/1.72
% 8.25/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 8.25/1.72
% 8.25/1.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.25/1.72
% 8.25/1.72
%------------------------------------------------------------------------------