%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL099-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 01:02:51 PM UTC 2026
% Result : Unsatisfiable 2.75s 1.19s
% Output : CNFRefutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 12 unt; 2 def)
% Number of atoms : 171 ( 5 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 164 ( 87 ~; 77 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 101 ( 0 sgn 101 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X2,X0,X1] :
( member(pair(X0,X1),trancl(X2))
| ~ member(pair(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r_into_trancl) ).
fof(f8,axiom,
! [X0] : trans(trancl(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_trancl) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( member(pair(X1,X3),X0)
| ~ member(pair(X2,X3),X0)
| ~ member(pair(X1,X2),X0)
| ~ trans(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transD) ).
fof(f10,axiom,
! [X2,X3,X0,X1] :
( member(pair(X3,diamond_strip_lemmaD_sk1(X1,X2,X3,X0)),trancl(X0))
| ~ member(pair(X1,X3),X0)
| ~ member(pair(X1,X2),trancl(X0))
| ~ diamond(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD1) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( member(pair(X2,diamond_strip_lemmaD_sk1(X1,X2,X3,X0)),X0)
| ~ member(pair(X1,X3),X0)
| ~ member(pair(X1,X2),trancl(X0))
| ~ diamond(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD2) ).
fof(f12,axiom,
diamond(r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_1h1) ).
fof(f13,axiom,
member(pair(y,ya),r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_1h2) ).
fof(f14,negated_conjecture,
member(pair(y,yp),trancl(r)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_1c1) ).
fof(f15,negated_conjecture,
! [X0] :
( ~ member(pair(yp,X0),trancl(r))
| ~ member(pair(ya,X0),trancl(r)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_1c2) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(pair(X0,X1),trancl(X2))
| ~ member(pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_70,plain,
! [X0: $i] : trans(trancl(X0)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(pair(X0,X3),X2)
| ~ trans(X2)
| ~ member(pair(X1,X3),X2)
| ~ member(pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(pair(X3,diamond_strip_lemmaD_sk1(X0,X1,X3,X2)),trancl(X2))
| ~ diamond(X2)
| ~ member(pair(X0,X3),X2)
| ~ member(pair(X0,X1),trancl(X2)) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(pair(X1,diamond_strip_lemmaD_sk1(X0,X1,X3,X2)),X2)
| ~ diamond(X2)
| ~ member(pair(X0,X3),X2)
| ~ member(pair(X0,X1),trancl(X2)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_74,plain,
diamond(r),
inference(cnf_transformation,[],[f12]) ).
tcf(c_75,plain,
member(pair(y,ya),r),
inference(cnf_transformation,[],[f13]) ).
tcf(c_76,negated_conjecture,
member(pair(y,yp),trancl(r)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_77,negated_conjecture,
! [X0: $i] :
( ~ member(pair(yp,X0),trancl(r))
| ~ member(pair(ya,X0),trancl(r)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(pair(X2,X4),X1)
| ~ member(pair(X3,X4),X1)
| ~ member(pair(X2,X3),X1)
| ( trancl(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_71]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(pair(X0,X3),trancl(X2))
| ~ member(pair(X1,X3),trancl(X2))
| ~ member(pair(X0,X1),trancl(X2)) ),
inference(unflattening,[status(thm)],[c_186]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(pair(X2,diamond_strip_lemmaD_sk1(X1,X2,X3,X0)),X0)
| ~ member(pair(X1,X3),X0)
| ~ member(pair(X1,X2),trancl(X0))
| ( X0 != r ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_74]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(pair(X1,diamond_strip_lemmaD_sk1(X0,X1,X2,r)),r)
| ~ member(pair(X0,X2),r)
| ~ member(pair(X0,X1),trancl(r)) ),
inference(unflattening,[status(thm)],[c_200]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(pair(X3,diamond_strip_lemmaD_sk1(X1,X2,X3,X0)),trancl(X0))
| ~ member(pair(X1,X3),X0)
| ~ member(pair(X1,X2),trancl(X0))
| ( X0 != r ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_74]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(pair(X2,diamond_strip_lemmaD_sk1(X0,X1,X2,r)),trancl(r))
| ~ member(pair(X0,X2),r)
| ~ member(pair(X0,X1),trancl(r)) ),
inference(unflattening,[status(thm)],[c_212]) ).
tcf(c_313,definition,
iPr_def_10 = trancl(r),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_314,definition,
iPr_def_11 = pair(y,yp),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_315,negated_conjecture,
! [X0: $i] :
( ~ member(pair(yp,X0),iPr_def_10)
| ~ member(pair(ya,X0),iPr_def_10) ),
inference(demodulation,[status(thm)],[c_77,c_313]) ).
tcf(c_316,negated_conjecture,
member(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_76,c_314]) ).
tcf(c_511,plain,
! [X0: $i,X1: $i] :
( member(pair(X0,X1),iPr_def_10)
| ~ member(pair(X0,X1),r) ),
inference(superposition,[status(thm)],[c_313,c_69]) ).
tcf(c_667,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(pair(X1,diamond_strip_lemmaD_sk1(X0,X1,X2,r)),r)
| ~ member(pair(X0,X2),r)
| ~ member(pair(X0,X1),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_201,c_313]) ).
tcf(c_677,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(pair(X1,diamond_strip_lemmaD_sk1(X0,X1,X2,r)),iPr_def_10)
| ~ member(pair(X0,X2),r)
| ~ member(pair(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_667,c_511]) ).
tcf(c_945,plain,
! [X0: $i,X1: $i] :
( member(pair(y,X0),trancl(X1))
| ~ member(iPr_def_11,trancl(X1))
| ~ member(pair(yp,X0),trancl(X1)) ),
inference(superposition,[status(thm)],[c_314,c_187]) ).
tcf(c_946,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(pair(X2,X1),trancl(r))
| ~ member(pair(X2,X0),iPr_def_10)
| ~ member(pair(X0,X1),trancl(r)) ),
inference(superposition,[status(thm)],[c_313,c_187]) ).
tcf(c_950,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(pair(X2,X1),iPr_def_10)
| ~ member(pair(X2,X0),iPr_def_10)
| ~ member(pair(X0,X1),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_946,c_313]) ).
tcf(c_1070,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(pair(X2,diamond_strip_lemmaD_sk1(X0,X1,X2,r)),iPr_def_10)
| ~ member(pair(X0,X2),r)
| ~ member(pair(X0,X1),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_213,c_313]) ).
tcf(c_1081,plain,
! [X0: $i,X1: $i] :
( ~ member(pair(X0,ya),r)
| ~ member(pair(X0,X1),iPr_def_10)
| ~ member(pair(yp,diamond_strip_lemmaD_sk1(X0,X1,ya,r)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_1070,c_315]) ).
tcf(c_1290,plain,
! [X0: $i,X1: $i] :
( member(pair(y,X0),trancl(X1))
| ~ member(iPr_def_11,trancl(X1))
| ~ member(pair(yp,X0),X1) ),
inference(superposition,[status(thm)],[c_69,c_945]) ).
tcf(c_1349,plain,
! [X0: $i] :
( member(pair(y,X0),iPr_def_10)
| ~ member(iPr_def_11,trancl(r))
| ~ member(pair(yp,X0),r) ),
inference(superposition,[status(thm)],[c_313,c_1290]) ).
tcf(c_1351,plain,
! [X0: $i] :
( member(pair(y,X0),iPr_def_10)
| ~ member(iPr_def_11,iPr_def_10)
| ~ member(pair(yp,X0),r) ),
inference(light_normalisation,[status(thm)],[c_1349,c_313]) ).
tcf(c_1352,plain,
! [X0: $i] :
( member(pair(y,X0),iPr_def_10)
| ~ member(pair(yp,X0),r) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1351,c_316]) ).
tcf(c_1749,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(pair(X1,diamond_strip_lemmaD_sk1(X0,X1,X2,r)),r)
| ~ member(pair(X0,X2),r)
| ~ member(pair(X0,X1),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_201,c_313]) ).
tcf(c_1760,plain,
! [X0: $i,X1: $i] :
( member(pair(y,diamond_strip_lemmaD_sk1(X0,yp,X1,r)),iPr_def_10)
| ~ member(pair(X0,yp),iPr_def_10)
| ~ member(pair(X0,X1),r) ),
inference(superposition,[status(thm)],[c_1749,c_1352]) ).
tcf(c_2627,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(pair(X2,diamond_strip_lemmaD_sk1(X0,yp,X1,r)),iPr_def_10)
| ~ member(pair(X2,y),iPr_def_10)
| ~ member(pair(X0,yp),iPr_def_10)
| ~ member(pair(X0,X1),r) ),
inference(superposition,[status(thm)],[c_1760,c_950]) ).
tcf(c_3586,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(pair(X2,diamond_strip_lemmaD_sk1(X0,X1,X2,r)),iPr_def_10)
| ~ member(pair(X0,X2),r)
| ~ member(pair(X0,X1),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_213,c_313]) ).
tcf(c_3597,plain,
! [X0: $i,X1: $i] :
( ~ member(pair(X0,ya),r)
| ~ member(pair(X0,X1),iPr_def_10)
| ~ member(pair(yp,diamond_strip_lemmaD_sk1(X0,X1,ya,r)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3586,c_315]) ).
tcf(c_4730,plain,
! [X0: $i] :
( ~ member(pair(X0,yp),iPr_def_10)
| ~ member(pair(X0,ya),r) ),
inference(superposition,[status(thm)],[c_677,c_1081]) ).
tcf(c_4831,plain,
! [X0: $i] :
( ~ member(pair(yp,y),iPr_def_10)
| ~ member(pair(X0,yp),iPr_def_10)
| ~ member(pair(X0,ya),r) ),
inference(superposition,[status(thm)],[c_2627,c_3597]) ).
tcf(c_5163,plain,
! [X0: $i] :
( ~ member(pair(X0,ya),r)
| ~ member(pair(X0,yp),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_4831,c_4730]) ).
tcf(c_5164,plain,
! [X0: $i] :
( ~ member(pair(X0,yp),iPr_def_10)
| ~ member(pair(X0,ya),r) ),
inference(renaming,[status(thm)],[c_5163]) ).
tcf(c_5169,plain,
( ~ member(iPr_def_11,iPr_def_10)
| ~ member(pair(y,ya),r) ),
inference(superposition,[status(thm)],[c_314,c_5164]) ).
tcf(c_5170,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5169,c_316,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL099-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n008.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 : Fri Sep 25 07:35:39 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...
% 2.75/1.19 % SZS status Started for theBenchmark.p
% 2.75/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 2.75/1.19
% 2.75/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.75/1.19
% 2.75/1.19 % ------ iProver source info
% 2.75/1.19
% 2.75/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 2.75/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.75/1.19 % git: non_committed_changes: false
% 2.75/1.19
% 2.75/1.19 % ------ Parsing...% successful
% 2.75/1.19
% 2.75/1.19
% 2.75/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.75/1.19
% 2.75/1.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 2.75/1.19
% 2.75/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.75/1.19
% 2.75/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.75/1.19 % ------ Proving...
% 2.75/1.19 % ------ Problem Properties
% 2.75/1.19
% 2.75/1.19 %
% 2.75/1.19 % clauses 14
% 2.75/1.19 % conjectures 2
% 2.75/1.19 % EPR 2
% 2.75/1.19 % Horn 14
% 2.75/1.19 % unary 7
% 2.75/1.19 % binary 4
% 2.75/1.19 % lits 24
% 2.75/1.19 % lits eq 9
% 2.75/1.19 % fd_pure 0
% 2.75/1.19 % fd_pseudo 0
% 2.75/1.19 % fd_cond 0
% 2.75/1.19 % fd_pseudo_cond 2
% 2.75/1.19 % AC symbols 0
% 2.75/1.19
% 2.75/1.19 % ------ Schedule dynamic 5 is on
% 2.75/1.19
% 2.75/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.75/1.19
% 2.75/1.19
% 2.75/1.19 % ------
% 2.75/1.19 % Current options:
% 2.75/1.19 % ------
% 2.75/1.19
% 2.75/1.19
% 2.75/1.19 %
% 2.75/1.19
% 2.75/1.19 % ------ Proving...
% 2.75/1.19 %
% 2.75/1.19
% 2.75/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 2.75/1.19
% 2.75/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.75/1.19
% 2.75/1.19
%------------------------------------------------------------------------------