%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL104-2 : 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 : 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 01:02:52 PM UTC 2026
% Result : Unsatisfiable 2.54s 1.52s
% Output : CNFRefutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 38 ( 22 unt; 8 def)
% Number of atoms : 133 ( 8 equ)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 45 ( 24 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 11 ( 9 usr; 9 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_in(c_Pair(v_y,v_za,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f2,negated_conjecture,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_x),c_Comb_Ocomb_Oop_A_D_D(v_z,v_y),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3,negated_conjecture,
~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_x),c_Comb_Ocomb_Oop_A_D_D(v_z,v_za),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f4,axiom,
! [X2,X0,X1] :
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X2,X0),c_Comb_Ocomb_Oop_A_D_D(X2,X1),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X0,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Ocontract_OAp2_0) ).
fof(f5,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f6,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__trans_0) ).
tcf(c_55,negated_conjecture,
c_in(c_Pair(v_y,v_za,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(cnf_transformation,[],[f1]) ).
tcf(c_56,negated_conjecture,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_x),c_Comb_Ocomb_Oop_A_D_D(v_z,v_y),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_57,negated_conjecture,
~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z,v_x),c_Comb_Ocomb_Oop_A_D_D(v_z,v_za),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X2,X0),c_Comb_Ocomb_Oop_A_D_D(X2,X1),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X0,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_59,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,[],[f5]) ).
tcf(c_60,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,[],[f6]) ).
tcf(c_83,definition,
iPr_def_10 = c_Comb_Ocomb_Oop_A_D_D(v_z,v_x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_84,definition,
iPr_def_11 = c_Comb_Ocomb_Oop_A_D_D(v_z,v_za),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_85,definition,
iPr_def_12 = c_Pair(iPr_def_10,iPr_def_11,tc_Comb_Ocomb,tc_Comb_Ocomb),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_86,definition,
iPr_def_13 = c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_87,definition,
iPr_def_14 = tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_88,definition,
iPr_def_15 = c_Comb_Ocomb_Oop_A_D_D(v_z,v_y),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_89,definition,
iPr_def_16 = c_Pair(iPr_def_10,iPr_def_15,tc_Comb_Ocomb,tc_Comb_Ocomb),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_90,definition,
iPr_def_17 = c_Pair(v_y,v_za,tc_Comb_Ocomb,tc_Comb_Ocomb),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_91,negated_conjecture,
~ c_in(iPr_def_12,iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_57,c_87,c_86,c_84,c_83,c_85]) ).
tcf(c_92,negated_conjecture,
c_in(iPr_def_16,iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_56,c_88,c_89]) ).
tcf(c_93,negated_conjecture,
c_in(iPr_def_17,c_Comb_Ocontract,iPr_def_14),
inference(demodulation,[status(thm)],[c_55,c_90]) ).
tcf(c_276,plain,
! [X0: $i] :
( c_in(X0,iPr_def_13,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(X0,c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(superposition,[status(thm)],[c_86,c_59]) ).
tcf(c_281,plain,
! [X0: $i] :
( c_in(X0,iPr_def_13,iPr_def_14)
| ~ c_in(X0,c_Comb_Ocontract,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_276,c_87]) ).
tcf(c_286,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X2,X0),c_Comb_Ocomb_Oop_A_D_D(X2,X1),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,iPr_def_14)
| ~ c_in(c_Pair(X0,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_58,c_87]) ).
tcf(c_294,plain,
! [X0: $i] :
( c_in(c_Pair(iPr_def_15,c_Comb_Ocomb_Oop_A_D_D(v_z,X0),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,iPr_def_14)
| ~ c_in(c_Pair(v_y,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,iPr_def_14) ),
inference(superposition,[status(thm)],[c_88,c_286]) ).
tcf(c_368,plain,
( c_in(c_Pair(iPr_def_15,iPr_def_11,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,iPr_def_14)
| ~ c_in(c_Pair(v_y,v_za,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,iPr_def_14) ),
inference(superposition,[status(thm)],[c_84,c_294]) ).
tcf(c_370,plain,
( c_in(c_Pair(iPr_def_15,iPr_def_11,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,iPr_def_14)
| ~ c_in(iPr_def_17,c_Comb_Ocontract,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_368,c_90]) ).
tcf(c_371,plain,
c_in(c_Pair(iPr_def_15,iPr_def_11,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_370,c_93]) ).
tcf(c_379,plain,
c_in(c_Pair(iPr_def_15,iPr_def_11,tc_Comb_Ocomb,tc_Comb_Ocomb),iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_371,c_281]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X0,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),iPr_def_13,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X0,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(superposition,[status(thm)],[c_86,c_60]) ).
tcf(c_437,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X0,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),iPr_def_13,iPr_def_14)
| ~ c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),iPr_def_13,iPr_def_14)
| ~ c_in(c_Pair(X0,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),iPr_def_13,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_419,c_86,c_87]) ).
tcf(c_602,plain,
! [X0: $i] :
( c_in(c_Pair(iPr_def_10,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),iPr_def_13,iPr_def_14)
| ~ c_in(iPr_def_16,iPr_def_13,iPr_def_14)
| ~ c_in(c_Pair(iPr_def_15,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),iPr_def_13,iPr_def_14) ),
inference(superposition,[status(thm)],[c_89,c_437]) ).
tcf(c_605,plain,
! [X0: $i] :
( c_in(c_Pair(iPr_def_10,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),iPr_def_13,iPr_def_14)
| ~ c_in(c_Pair(iPr_def_15,X0,tc_Comb_Ocomb,tc_Comb_Ocomb),iPr_def_13,iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_602,c_92]) ).
tcf(c_639,plain,
c_in(c_Pair(iPr_def_10,iPr_def_11,tc_Comb_Ocomb,tc_Comb_Ocomb),iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_379,c_605]) ).
tcf(c_640,plain,
c_in(iPr_def_12,iPr_def_13,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_639,c_85]) ).
tcf(c_641,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_640,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL104-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.44 % Computer : n008.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 07:36:39 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.51 Running first-order theorem proving
% 0.19/0.51 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
% 0.28/0.52
% 0.28/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.28/0.52
% 0.28/0.53 % Detected problem language: tptp
% 0.28/0.54 % Proving...
% 2.54/1.52 % SZS status Started for theBenchmark.p
% 2.54/1.52 % SZS status Unsatisfiable for theBenchmark.p
% 2.54/1.52
% 2.54/1.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.54/1.52
% 2.54/1.52 % ------ iProver source info
% 2.54/1.52
% 2.54/1.52 % git: date: 2026-07-19 20:42:38 +0200
% 2.54/1.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.54/1.52 % git: non_committed_changes: false
% 2.54/1.52
% 2.54/1.52 % ------ Parsing...% successful
% 2.54/1.52
% 2.54/1.52
% 2.54/1.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.54/1.52
% 2.54/1.52 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.54/1.52
% 2.54/1.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.54/1.52
% 2.54/1.52 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.54/1.52 % ------ Proving...
% 2.54/1.52 % ------ Problem Properties
% 2.54/1.52
% 2.54/1.52 %
% 2.54/1.52 % clauses 14
% 2.54/1.52 % conjectures 3
% 2.54/1.52 % EPR 3
% 2.54/1.52 % Horn 14
% 2.54/1.52 % unary 11
% 2.54/1.52 % binary 2
% 2.54/1.52 % lits 18
% 2.54/1.52 % lits eq 8
% 2.54/1.52 % fd_pure 0
% 2.54/1.52 % fd_pseudo 0
% 2.54/1.52 % fd_cond 0
% 2.54/1.52 % fd_pseudo_cond 0
% 2.54/1.52 % AC symbols 0
% 2.54/1.52
% 2.54/1.52 % ------ Schedule dynamic 5 is on
% 2.54/1.52
% 2.54/1.52 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.54/1.52
% 2.54/1.52
% 2.54/1.52 % ------
% 2.54/1.52 % Current options:
% 2.54/1.52 % ------
% 2.54/1.52
% 2.54/1.52
% 2.54/1.52 %
% 2.54/1.52
% 2.54/1.52 % ------ Proving...
% 2.54/1.52 %
% 2.54/1.52
% 2.54/1.52 % SZS status Unsatisfiable for theBenchmark.p
% 2.54/1.52
% 2.54/1.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.54/1.52
% 2.54/1.52
%------------------------------------------------------------------------------