%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SCT126+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 02:40:47 PM UTC 2026
% Result : Theorem 10.87s 7.32s
% Output : CNFRefutation 10.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 13 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 2 =>; 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 : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096Q_A_058_AProf_096) ).
fof(f24,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I1_J) ).
fof(f39,axiom,
! [X0,X1,X2,X3,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X4)),X3),c_FuncSet_OPi(X5,X4,X2,c_COMBK(tc_fun(X4,tc_HOL_Obool),X5,X1))))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X0),X2))
=> hBOOL(hAPP(hAPP(c_member(X4),hAPP(X3,X0)),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__mem) ).
fof(f525,conjecture,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f526,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(negated_conjecture,[status(cth)],[f525]) ).
fof(f527,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(flattening,[],[f526]) ).
fof(f579,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X4)),X3),c_FuncSet_OPi(X5,X4,X2,c_COMBK(tc_fun(X4,tc_HOL_Obool),X5,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X0),X2))
| hBOOL(hAPP(hAPP(c_member(X4),hAPP(X3,X0)),X1)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f580,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X4)),X3),c_FuncSet_OPi(X5,X4,X2,c_COMBK(tc_fun(X4,tc_HOL_Obool),X5,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X0),X2))
| hBOOL(hAPP(hAPP(c_member(X4),hAPP(X3,X0)),X1)) ),
inference(flattening,[],[f579]) ).
fof(f1190,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(cnf_transformation,[],[f4]) ).
fof(f1242,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
inference(cnf_transformation,[],[f24]) ).
fof(f1278,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X4)),X3),c_FuncSet_OPi(X5,X4,X2,c_COMBK(tc_fun(X4,tc_HOL_Obool),X5,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X0),X2))
| hBOOL(hAPP(hAPP(c_member(X4),hAPP(X3,X0)),X1)) ),
inference(cnf_transformation,[],[f580]) ).
fof(f1926,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(cnf_transformation,[],[f527]) ).
tcf(c_53,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(cnf_transformation,[],[f1190]) ).
tcf(c_94,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
inference(cnf_transformation,[],[f1242]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X5)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X5),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,c_COMBK(tc_fun(X1,tc_HOL_Obool),X0,X4)))) ),
inference(cnf_transformation,[],[f1278]) ).
tcf(c_759,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(cnf_transformation,[],[f1926]) ).
tcf(c_14206,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,X0)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X0),c_Arrow__Order__Mirabelle_OProf)) ),
inference(superposition,[status(thm)],[c_94,c_126]) ).
tcf(c_16384,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(superposition,[status(thm)],[c_53,c_14206]) ).
tcf(c_16388,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_759,c_16384]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT126+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.39 % Computer : n011.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Thu Sep 24 08:49:32 UTC 2026
% 0.16/5.40 % CPUTime :
% 0.16/5.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 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
% 0.16/5.45
% 0.16/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.45
% 0.16/5.45 % Detected problem language: tptp
% 0.16/5.46 % Proving...
% 10.87/7.32 % SZS status Started for theBenchmark.p
% 10.87/7.32 % SZS status Theorem for theBenchmark.p
% 10.87/7.32
% 10.87/7.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.87/7.32
% 10.87/7.32 % ------ iProver source info
% 10.87/7.32
% 10.87/7.32 % git: date: 2026-07-19 20:42:38 +0200
% 10.87/7.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.87/7.32 % git: non_committed_changes: false
% 10.87/7.32
% 10.87/7.32 % ------ Parsing...
% 10.87/7.32 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.87/7.32 % ------ Proving...
% 10.87/7.32 % ------ Problem Properties
% 10.87/7.32
% 10.87/7.32 %
% 10.87/7.32 % clauses 711
% 10.87/7.32 % conjectures 1
% 10.87/7.32 % EPR 29
% 10.87/7.32 % Horn 566
% 10.87/7.32 % unary 169
% 10.87/7.32 % binary 312
% 10.87/7.32 % lits 1577
% 10.87/7.32 % lits eq 361
% 10.87/7.32 % fd_pure 0
% 10.87/7.32 % fd_pseudo 0
% 10.87/7.32 % fd_cond 0
% 10.87/7.32 % fd_pseudo_cond 96
% 10.87/7.32 % AC symbols 0
% 10.87/7.32
% 10.87/7.32 % ------ Input Options Time Limit: Unbounded
% 10.87/7.32
% 10.87/7.32
% 10.87/7.32 % ------
% 10.87/7.32 % Current options:
% 10.87/7.32 % ------
% 10.87/7.32
% 10.87/7.32
% 10.87/7.32 %
% 10.87/7.32
% 10.87/7.32 % ------ Proving...
% 10.87/7.32 %
% 10.87/7.32
% 10.87/7.32 % ------ Proving...
% 10.87/7.32 %
% 10.87/7.32
% 10.87/7.32 % SZS status Theorem for theBenchmark.p
% 10.87/7.32
% 10.87/7.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.87/7.32
% 10.87/7.32
%------------------------------------------------------------------------------