%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET820-2 : 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 : n010.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 02:48:39 PM UTC 2026
% Result : Unsatisfiable 2.33s 1.44s
% Output : CNFRefutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 34 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 18 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 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 : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 40 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f2,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( X0 = X1
| c_in(X0,X2,X3)
| ~ c_in(X0,c_insert(X1,X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f4,negated_conjecture,
v_P(v_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f5,negated_conjecture,
! [X0,X1] :
( c_in(v_x(X1),X1,tc_IntDef_Oint)
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f6,negated_conjecture,
! [X0,X1] :
( ~ v_P(v_x(X1))
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : ~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[],[f2]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X2,X3)
| ( X0 = X1 )
| ~ c_in(X0,c_insert(X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_58,negated_conjecture,
v_P(v_a),
inference(cnf_transformation,[],[f4]) ).
tcf(c_59,negated_conjecture,
! [X0: $i,X1: $i] :
( c_in(v_x(X1),X1,tc_IntDef_Oint)
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_60,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ v_P(v_x(X1))
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( ~ c_in(X1,X0,tc_IntDef_Oint)
| ( v_x(X0) != v_a ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_60]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( ~ c_in(X1,X0,tc_IntDef_Oint)
| ( v_x(X0) != v_a ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_148,negated_conjecture,
! [X0: $i,X1: $i] :
( c_in(v_x(X1),X1,tc_IntDef_Oint)
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i] : c_in(v_x(c_insert(X0,X1,tc_IntDef_Oint)),c_insert(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint),
inference(superposition,[status(thm)],[c_56,c_148]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] :
( c_in(v_x(c_insert(X0,X1,tc_IntDef_Oint)),X1,tc_IntDef_Oint)
| ( v_x(c_insert(X0,X1,tc_IntDef_Oint)) = X0 ) ),
inference(superposition,[status(thm)],[c_235,c_57]) ).
tcf(c_253,plain,
! [X0: $i] : v_x(c_insert(X0,c_emptyset,tc_IntDef_Oint)) = X0,
inference(superposition,[status(thm)],[c_245,c_55]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i] :
( ~ c_in(X1,c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint)
| ( X0 != v_a ) ),
inference(superposition,[status(thm)],[c_253,c_147]) ).
tcf(c_384,plain,
! [X0: $i] : ~ c_in(X0,c_insert(v_a,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint),
inference(equality_resolution,[status(thm)],[c_275]) ).
tcf(c_386,plain,
$false,
inference(superposition,[status(thm)],[c_56,c_384]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET820-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.44 % Computer : n010.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Thu Sep 24 12:03:43 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.27/0.51 Running first-order theorem proving
% 0.27/0.51 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
% 0.27/0.52
% 0.27/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.27/0.52
% 0.27/0.52 % Detected problem language: tptp
% 0.27/0.54 % Proving...
% 2.33/1.44 % SZS status Started for theBenchmark.p
% 2.33/1.44 % SZS status Unsatisfiable for theBenchmark.p
% 2.33/1.44
% 2.33/1.44 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.33/1.44
% 2.33/1.44 % ------ iProver source info
% 2.33/1.44
% 2.33/1.44 % git: date: 2026-07-19 20:42:38 +0200
% 2.33/1.44 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.33/1.44 % git: non_committed_changes: false
% 2.33/1.44
% 2.33/1.44 % ------ Parsing...% successful
% 2.33/1.44
% 2.33/1.44
% 2.33/1.44 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.33/1.44
% 2.33/1.44 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.33/1.44
% 2.33/1.44 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.33/1.44
% 2.33/1.44 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.33/1.44 % ------ Proving...
% 2.33/1.44 % ------ Problem Properties
% 2.33/1.44
% 2.33/1.44 %
% 2.33/1.44 % clauses 5
% 2.33/1.44 % conjectures 1
% 2.33/1.44 % EPR 1
% 2.33/1.44 % Horn 4
% 2.33/1.44 % unary 2
% 2.33/1.44 % binary 2
% 2.33/1.44 % lits 9
% 2.33/1.44 % lits eq 2
% 2.33/1.44 % fd_pure 0
% 2.33/1.44 % fd_pseudo 0
% 2.33/1.44 % fd_cond 0
% 2.33/1.44 % fd_pseudo_cond 1
% 2.33/1.44 % AC symbols 0
% 2.33/1.44
% 2.33/1.44 % ------ Schedule dynamic 5 is on
% 2.33/1.44
% 2.33/1.44 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.33/1.44
% 2.33/1.44
% 2.33/1.44 % ------
% 2.33/1.44 % Current options:
% 2.33/1.44 % ------
% 2.33/1.44
% 2.33/1.44
% 2.33/1.44 %
% 2.33/1.44
% 2.33/1.44 % ------ Proving...
% 2.33/1.44 %
% 2.33/1.44
% 2.33/1.44 % SZS status Unsatisfiable for theBenchmark.p
% 2.33/1.44
% 2.33/1.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.33/1.44
% 2.33/1.44
%------------------------------------------------------------------------------