%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL123-2 : 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 01:02:57 PM UTC 2026
% Result : Unsatisfiable 2.98s 1.29s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 11 unt; 4 def)
% Number of atoms : 161 ( 4 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 111 ( 60 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 7 ( 5 usr; 5 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 66 ( 0 sgn 66 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,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) ).
fof(f3,negated_conjecture,
c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f4,negated_conjecture,
c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f5,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(v_x,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(X0,v_xaa(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f6,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(v_x,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_y,v_xaa(X0),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f7,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(v_xb,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),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f8,negated_conjecture,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X1,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(X0,v_xa(X1,X0,X2),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f9,negated_conjecture,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X1,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(X0,v_xa(X1,X2,X0),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).
tcf(c_58,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,[],[f1]) ).
tcf(c_59,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,[],[f2]) ).
tcf(c_60,negated_conjecture,
c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_61,negated_conjecture,
c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] :
( c_in(c_Pair(X0,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,X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_63,negated_conjecture,
! [X0: $i] :
( c_in(c_Pair(v_y,v_xaa(X0),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_64,negated_conjecture,
! [X0: $i] :
( ~ c_in(c_Pair(v_z,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xb,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_65,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X1,v_xa(X0,X1,X2),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),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_66,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X1,v_xa(X0,X2,X1),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),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_110,definition,
iPr_def_10 = tc_prod(t_a,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_111,definition,
iPr_def_11 = c_Transitive__Closure_Ortrancl(v_r,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_112,definition,
iPr_def_12 = c_Pair(v_x,v_xb,t_a,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_113,definition,
iPr_def_13 = c_Pair(v_y,v_z,t_a,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_114,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X1,v_xa(X0,X2,X1),t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(X0,X2,t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(X0,X1,t_a,t_a),v_r,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_66,c_110]) ).
tcf(c_115,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X1,v_xa(X0,X1,X2),t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(X0,X2,t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(X0,X1,t_a,t_a),v_r,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_116,negated_conjecture,
! [X0: $i] :
( ~ c_in(c_Pair(v_xb,X0,t_a,t_a),iPr_def_11,iPr_def_10)
| ~ c_in(c_Pair(v_z,X0,t_a,t_a),v_r,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_64,c_111]) ).
tcf(c_117,negated_conjecture,
! [X0: $i] :
( c_in(c_Pair(v_y,v_xaa(X0),t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(v_x,X0,t_a,t_a),v_r,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_118,negated_conjecture,
! [X0: $i] :
( c_in(c_Pair(X0,v_xaa(X0),t_a,t_a),iPr_def_11,iPr_def_10)
| ~ c_in(c_Pair(v_x,X0,t_a,t_a),v_r,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_119,negated_conjecture,
c_in(iPr_def_12,v_r,iPr_def_10),
inference(demodulation,[status(thm)],[c_61,c_112]) ).
tcf(c_120,negated_conjecture,
c_in(iPr_def_13,v_r,iPr_def_10),
inference(demodulation,[status(thm)],[c_60,c_113]) ).
tcf(c_340,plain,
! [X0: $i] :
( c_in(X0,iPr_def_11,tc_prod(t_a,t_a))
| ~ c_in(X0,v_r,tc_prod(t_a,t_a)) ),
inference(superposition,[status(thm)],[c_111,c_58]) ).
tcf(c_345,plain,
! [X0: $i] :
( c_in(X0,iPr_def_11,iPr_def_10)
| ~ c_in(X0,v_r,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_340,c_110]) ).
tcf(c_354,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X1,v_xa(X0,X2,X1),t_a,t_a),iPr_def_11,iPr_def_10)
| ~ c_in(c_Pair(X0,X2,t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(X0,X1,t_a,t_a),v_r,iPr_def_10) ),
inference(superposition,[status(thm)],[c_114,c_345]) ).
tcf(c_432,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X0,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),iPr_def_11,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(superposition,[status(thm)],[c_111,c_59]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X0,X2,t_a,t_a),iPr_def_11,iPr_def_10)
| ~ c_in(c_Pair(X1,X2,t_a,t_a),iPr_def_11,iPr_def_10)
| ~ c_in(c_Pair(X0,X1,t_a,t_a),iPr_def_11,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_432,c_110,c_111]) ).
tcf(c_503,plain,
! [X0: $i,X1: $i] :
( c_in(c_Pair(X0,X1,t_a,t_a),iPr_def_11,iPr_def_10)
| ~ c_in(c_Pair(v_x,X0,t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(v_xaa(X0),X1,t_a,t_a),iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_118,c_446]) ).
tcf(c_645,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X1,v_xa(X0,X2,v_xaa(X1)),t_a,t_a),iPr_def_11,iPr_def_10)
| ~ c_in(c_Pair(v_x,X1,t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(X0,X2,t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(X0,v_xaa(X1),t_a,t_a),v_r,iPr_def_10) ),
inference(superposition,[status(thm)],[c_354,c_503]) ).
tcf(c_2760,plain,
! [X0: $i,X1: $i] :
( ~ c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(X0,X1,t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(X0,v_xaa(v_xb),t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(v_z,v_xa(X0,X1,v_xaa(v_xb)),t_a,t_a),v_r,iPr_def_10) ),
inference(superposition,[status(thm)],[c_645,c_116]) ).
tcf(c_2774,plain,
! [X0: $i,X1: $i] :
( ~ c_in(iPr_def_12,v_r,iPr_def_10)
| ~ c_in(c_Pair(X0,X1,t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(X0,v_xaa(v_xb),t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(v_z,v_xa(X0,X1,v_xaa(v_xb)),t_a,t_a),v_r,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_2760,c_112]) ).
tcf(c_2775,plain,
! [X0: $i,X1: $i] :
( ~ c_in(c_Pair(X0,X1,t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(X0,v_xaa(v_xb),t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(v_z,v_xa(X0,X1,v_xaa(v_xb)),t_a,t_a),v_r,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2774,c_119]) ).
tcf(c_2960,plain,
! [X0: $i] :
( ~ c_in(c_Pair(X0,v_z,t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(X0,v_xaa(v_xb),t_a,t_a),v_r,iPr_def_10) ),
inference(superposition,[status(thm)],[c_115,c_2775]) ).
tcf(c_2968,plain,
( ~ c_in(c_Pair(v_x,v_xb,t_a,t_a),v_r,iPr_def_10)
| ~ c_in(c_Pair(v_y,v_z,t_a,t_a),v_r,iPr_def_10) ),
inference(superposition,[status(thm)],[c_117,c_2960]) ).
tcf(c_2969,plain,
( ~ c_in(iPr_def_13,v_r,iPr_def_10)
| ~ c_in(iPr_def_12,v_r,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_2968,c_112,c_113]) ).
tcf(c_2970,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2969,c_120,c_119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL123-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/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 07:42:09 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 2.98/1.29 % SZS status Started for theBenchmark.p
% 2.98/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.98/1.29
% 2.98/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.98/1.29
% 2.98/1.29 % ------ iProver source info
% 2.98/1.29
% 2.98/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.98/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.98/1.29 % git: non_committed_changes: false
% 2.98/1.29
% 2.98/1.29 % ------ Parsing...% successful
% 2.98/1.29
% 2.98/1.29
% 2.98/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.98/1.29
% 2.98/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.98/1.29
% 2.98/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.98/1.29
% 2.98/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.98/1.29 % ------ Proving...
% 2.98/1.29 % ------ Problem Properties
% 2.98/1.29
% 2.98/1.29 %
% 2.98/1.29 % clauses 13
% 2.98/1.29 % conjectures 7
% 2.98/1.29 % EPR 2
% 2.98/1.29 % Horn 13
% 2.98/1.29 % unary 6
% 2.98/1.29 % binary 4
% 2.98/1.29 % lits 23
% 2.98/1.29 % lits eq 4
% 2.98/1.29 % fd_pure 0
% 2.98/1.29 % fd_pseudo 0
% 2.98/1.29 % fd_cond 0
% 2.98/1.29 % fd_pseudo_cond 0
% 2.98/1.29 % AC symbols 0
% 2.98/1.29
% 2.98/1.29 % ------ Schedule dynamic 5 is on
% 2.98/1.29
% 2.98/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.98/1.29
% 2.98/1.29
% 2.98/1.29 % ------
% 2.98/1.29 % Current options:
% 2.98/1.29 % ------
% 2.98/1.29
% 2.98/1.29
% 2.98/1.29 %
% 2.98/1.29
% 2.98/1.29 % ------ Proving...
% 2.98/1.29 %
% 2.98/1.29
% 2.98/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.98/1.29
% 2.98/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.98/1.29
% 2.98/1.29
%------------------------------------------------------------------------------