%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL121-1 : 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 : 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 01:02:57 PM UTC 2026
% Result : Unsatisfiable 3.75s 1.38s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 7 unt; 0 def)
% Number of atoms : 84 ( 4 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 106 ( 56 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 73 ( 0 sgn 73 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
fof(f393,axiom,
! [X2,X0,X1] :
( c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(X0,X1,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f1445,axiom,
! [X2,X3,X0,X1,X4] :
( c_in(c_Pair(X3,c_Comb_Odiamond__strip__lemmaE__1(X0,X4,X3,X1),X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_Comb_Odiamond(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_0) ).
fof(f1446,axiom,
! [X2,X3,X0,X1,X4] :
( c_in(c_Pair(X4,c_Comb_Odiamond__strip__lemmaE__1(X0,X4,X3,X1),X1,X1),X0,tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_Comb_Odiamond(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_1) ).
fof(f1447,axiom,
! [X2,X3,X0,X1,X4] :
( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__trans_0) ).
fof(f1448,negated_conjecture,
c_Comb_Odiamond(v_r,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1450,negated_conjecture,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1451,negated_conjecture,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1452,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_ya,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f1453,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X0,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f1454,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(v_z,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
tcf(c_1424,negated_conjecture,
c_Comb_Odiamond(v_r,t_a),
inference(cnf_transformation,[],[f1448]) ).
tcf(c_1426,negated_conjecture,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[],[f1450]) ).
tcf(c_1427,negated_conjecture,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(cnf_transformation,[],[f1451]) ).
tcf(c_1428,negated_conjecture,
! [X0: $i] :
( c_in(c_Pair(v_ya,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f1452]) ).
tcf(c_1429,negated_conjecture,
! [X0: $i] :
( c_in(c_Pair(X0,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f1453]) ).
tcf(c_1430,negated_conjecture,
! [X0: $i] :
( ~ c_in(c_Pair(v_xaa,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f1454]) ).
tcf(c_1431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X1,c_Comb_Odiamond__strip__lemmaE__1(X3,X1,X4,X2),X2,X2),X3,tc_prod(X2,X2))
| ~ c_Comb_Odiamond(X3,X2)
| ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f1446]) ).
tcf(c_1432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X4,c_Comb_Odiamond__strip__lemmaE__1(X3,X1,X4,X2),X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_Comb_Odiamond(X3,X2)
| ~ c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f1445]) ).
tcf(c_1435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f1447]) ).
tcf(c_1437,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(X0,X1,tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f393]) ).
tcf(c_1554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X3,c_Comb_Odiamond__strip__lemmaE__1(X1,X3,X4,X0),X0,X0),X1,tc_prod(X0,X0))
| ~ c_in(c_Pair(X2,X4,X0,X0),X1,tc_prod(X0,X0))
| ~ c_in(c_Pair(X2,X3,X0,X0),c_Transitive__Closure_Ortrancl(X1,X0),tc_prod(X0,X0))
| ( X1 != v_r )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_1431,c_1424]) ).
tcf(c_1555,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X1,c_Comb_Odiamond__strip__lemmaE__1(v_r,X1,X2,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(unflattening,[status(thm)],[c_1554]) ).
tcf(c_1566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X4,c_Comb_Odiamond__strip__lemmaE__1(X1,X3,X4,X0),X0,X0),c_Transitive__Closure_Ortrancl(X1,X0),tc_prod(X0,X0))
| ~ c_in(c_Pair(X2,X4,X0,X0),X1,tc_prod(X0,X0))
| ~ c_in(c_Pair(X2,X3,X0,X0),c_Transitive__Closure_Ortrancl(X1,X0),tc_prod(X0,X0))
| ( X1 != v_r )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_1432,c_1424]) ).
tcf(c_1567,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X2,c_Comb_Odiamond__strip__lemmaE__1(v_r,X1,X2,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(unflattening,[status(thm)],[c_1566]) ).
tcf(c_1915,plain,
! [X0: $i,X1: $i] :
( c_in(c_Pair(v_x(X0),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(X0),X1,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(superposition,[status(thm)],[c_1428,c_1555]) ).
tcf(c_1939,plain,
! [X0: $i,X1: $i] :
( c_in(c_Pair(X1,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(X0),X1,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(superposition,[status(thm)],[c_1428,c_1567]) ).
tcf(c_2102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Pair(X0,X4,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
inference(superposition,[status(thm)],[c_1437,c_1435]) ).
tcf(c_2415,plain,
! [X0: $i] :
( ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(X0),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(superposition,[status(thm)],[c_1939,c_1430]) ).
tcf(c_2422,plain,
! [X0: $i] :
( ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xaa,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(X0),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2415,c_1426]) ).
tcf(c_3550,plain,
! [X0: $i,X1: $i] :
( c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(X0),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(superposition,[status(thm)],[c_1429,c_2102]) ).
tcf(c_4032,plain,
! [X0: $i] :
( c_in(c_Pair(v_xaa,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(superposition,[status(thm)],[c_1427,c_3550]) ).
tcf(c_4151,plain,
! [X0: $i] :
( ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(X0),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(superposition,[status(thm)],[c_4032,c_2422]) ).
tcf(c_5627,plain,
( ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(superposition,[status(thm)],[c_1915,c_4151]) ).
tcf(c_5630,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5627,c_1426,c_1427]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL121-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.41 % Computer : n011.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Fri Sep 25 07:41:28 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 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
% 0.16/0.48
% 0.16/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.48
% 0.16/0.49 % Detected problem language: tptp
% 0.23/0.50 % Proving...
% 3.75/1.38 % SZS status Started for theBenchmark.p
% 3.75/1.38 % SZS status Unsatisfiable for theBenchmark.p
% 3.75/1.38
% 3.75/1.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.75/1.38
% 3.75/1.38 % ------ iProver source info
% 3.75/1.38
% 3.75/1.38 % git: date: 2026-07-19 20:42:38 +0200
% 3.75/1.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.75/1.38 % git: non_committed_changes: false
% 3.75/1.38
% 3.75/1.38 % ------ Parsing...% successful
% 3.75/1.38
% 3.75/1.38
% 3.75/1.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.75/1.38
% 3.75/1.38 % ------ 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 %
% 3.75/1.38
% 3.75/1.38 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.75/1.38
% 3.75/1.38 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.75/1.38 % ------ Proving...
% 3.75/1.38 % ------ Problem Properties
% 3.75/1.38
% 3.75/1.38 %
% 3.75/1.38 % clauses 13
% 3.75/1.38 % conjectures 6
% 3.75/1.38 % EPR 0
% 3.75/1.38 % Horn 13
% 3.75/1.38 % unary 4
% 3.75/1.38 % binary 6
% 3.75/1.38 % lits 25
% 3.75/1.38 % lits eq 4
% 3.75/1.38 % fd_pure 0
% 3.75/1.38 % fd_pseudo 0
% 3.75/1.38 % fd_cond 0
% 3.75/1.38 % fd_pseudo_cond 2
% 3.75/1.38 % AC symbols 0
% 3.75/1.38
% 3.75/1.38 % ------ Schedule dynamic 5 is on
% 3.75/1.38
% 3.75/1.38 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.75/1.38
% 3.75/1.38
% 3.75/1.38 % ------
% 3.75/1.38 % Current options:
% 3.75/1.38 % ------
% 3.75/1.38
% 3.75/1.38
% 3.75/1.38 %
% 3.75/1.38
% 3.75/1.38 % ------ Proving...
% 3.75/1.38 %
% 3.75/1.38
% 3.75/1.38 % SZS status Unsatisfiable for theBenchmark.p
% 3.75/1.38
% 3.75/1.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.75/1.38
% 3.75/1.38
%------------------------------------------------------------------------------