%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET822-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 02:48:40 PM UTC 2026
% Result : Unsatisfiable 4.66s 2.29s
% Output : CNFRefutation 4.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 33 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 34 ( 21 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f227,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-2.ax',cls_Set_OinsertCI_1) ).
fof(f375,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ c_in(X0,c_insert(X1,c_emptyset,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OsingletonD__dest_0) ).
fof(f1434,negated_conjecture,
v_P(v_f(v_b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1435,negated_conjecture,
! [X0,X1] :
( c_in(v_x(X0,X1),X1,tc_IntDef_Oint)
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1436,negated_conjecture,
! [X0,X1] :
( ~ v_P(v_x(X0,X1))
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tcf(c_1584,plain,
! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[],[f227]) ).
tcf(c_1709,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ c_in(X0,c_insert(X1,c_emptyset,X2),X2) ),
inference(cnf_transformation,[],[f375]) ).
tcf(c_2000,negated_conjecture,
v_P(v_f(v_b)),
inference(cnf_transformation,[],[f1434]) ).
tcf(c_2001,negated_conjecture,
! [X0: $i,X1: $i] :
( c_in(v_x(X0,X1),X1,tc_IntDef_Oint)
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[],[f1435]) ).
tcf(c_2002,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ v_P(v_x(X0,X1))
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[],[f1436]) ).
tcf(c_2333,plain,
! [X0: $i,X1: $i] :
( ~ v_P(v_x(X0,X1))
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
inference(prop_impl_just,[status(thm)],[c_2002]) ).
tcf(c_8349,plain,
! [X0: $i,X1: $i] :
( ~ c_in(v_f(X0),X1,tc_IntDef_Oint)
| ( v_x(X0,X1) != v_f(v_b) ) ),
inference(resolution_lifted,[status(thm)],[c_2000,c_2333]) ).
tcf(c_9741,plain,
! [X0: $i,X1: $i] :
( ( v_x(X0,X1) != v_f(v_b) )
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
inference(prop_impl_just,[status(thm)],[c_8349]) ).
tcf(c_9742,plain,
! [X0: $i,X1: $i] :
( ~ c_in(v_f(X0),X1,tc_IntDef_Oint)
| ( v_x(X0,X1) != v_f(v_b) ) ),
inference(renaming,[status(thm)],[c_9741]) ).
tcf(c_13427,negated_conjecture,
! [X0: $i,X1: $i] :
( c_in(v_x(X0,X1),X1,tc_IntDef_Oint)
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
inference(demodulation,[status(thm)],[c_2001]) ).
tcf(c_19198,plain,
! [X0: $i,X1: $i] :
( ( v_x(X0,c_insert(X1,c_emptyset,tc_IntDef_Oint)) = X1 )
| ~ c_in(v_f(X0),c_insert(X1,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(superposition,[status(thm)],[c_13427,c_1709]) ).
tcf(c_19266,plain,
! [X0: $i] : v_x(X0,c_insert(v_f(X0),c_emptyset,tc_IntDef_Oint)) = v_f(X0),
inference(superposition,[status(thm)],[c_1584,c_19198]) ).
tcf(c_22462,plain,
! [X0: $i] :
( ~ c_in(v_f(X0),c_insert(v_f(X0),c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint)
| ( v_f(X0) != v_f(v_b) ) ),
inference(superposition,[status(thm)],[c_19266,c_9742]) ).
tcf(c_22463,plain,
! [X0: $i] : v_f(X0) != v_f(v_b),
inference(forward_subsumption_resolution,[status(thm)],[c_22462,c_1584]) ).
tcf(c_22465,plain,
$false,
inference(equality_resolution,[status(thm)],[c_22463]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET822-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n026.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 12:06:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 4.66/2.29 % SZS status Started for theBenchmark.p
% 4.66/2.29 % SZS status Unsatisfiable for theBenchmark.p
% 4.66/2.29
% 4.66/2.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.66/2.29
% 4.66/2.29 % ------ iProver source info
% 4.66/2.29
% 4.66/2.29 % git: date: 2026-07-19 20:42:38 +0200
% 4.66/2.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.66/2.29 % git: non_committed_changes: false
% 4.66/2.29
% 4.66/2.29 % ------ Parsing...% successful
% 4.66/2.29
% 4.66/2.29
% 4.66/2.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.66/2.29
% 4.66/2.29 % ------ Preprocessing... sup_sim: 1 sf_s rm: 18 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 0 sf_s rm: 31 0s sf_e pe_s pe_e %
% 4.66/2.29
% 4.66/2.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.66/2.29
% 4.66/2.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.66/2.29 % ------ Proving...
% 4.66/2.29 % ------ Problem Properties
% 4.66/2.29
% 4.66/2.29 %
% 4.66/2.29 % clauses 297
% 4.66/2.29 % conjectures 1
% 4.66/2.29 % EPR 26
% 4.66/2.29 % Horn 270
% 4.66/2.29 % unary 75
% 4.66/2.29 % binary 175
% 4.66/2.29 % lits 566
% 4.66/2.29 % lits eq 163
% 4.66/2.29 % fd_pure 0
% 4.66/2.29 % fd_pseudo 0
% 4.66/2.29 % fd_cond 21
% 4.66/2.29 % fd_pseudo_cond 40
% 4.66/2.29 % AC symbols 0
% 4.66/2.29
% 4.66/2.29 % ------ Schedule dynamic 5 is on
% 4.66/2.29
% 4.66/2.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.66/2.29
% 4.66/2.29
% 4.66/2.29 % ------
% 4.66/2.29 % Current options:
% 4.66/2.29 % ------
% 4.66/2.29
% 4.66/2.29
% 4.66/2.29 %
% 4.66/2.29
% 4.66/2.29 % ------ Proving...
% 4.66/2.29 %
% 4.66/2.29
% 4.66/2.29 % SZS status Unsatisfiable for theBenchmark.p
% 4.66/2.29
% 4.66/2.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.66/2.29
% 4.66/2.29
%------------------------------------------------------------------------------