%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP124-1.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.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 01:31:09 PM UTC 2026
% Result : Unsatisfiable 2.74s 1.22s
% Output : CNFRefutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 77 ( 25 unt; 0 def)
% Number of atoms : 223 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 267 ( 121 ~; 146 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 82 ( 0 sgn 82 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f6,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f7,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f11,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f13,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f14,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
fof(f16,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f17,axiom,
! [X0,X1] :
( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f19,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f20,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f21,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f23,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X1,X4)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2_2) ).
tcf(c_73,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equalish(X1,X4)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_74,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f21]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_4)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_79,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[],[f14]) ).
tcf(c_80,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[],[f11]) ).
tcf(c_82,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[],[f7]) ).
tcf(c_83,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f6]) ).
tcf(c_85,plain,
group_element(e_4),
inference(cnf_transformation,[],[f4]) ).
tcf(c_86,plain,
group_element(e_3),
inference(cnf_transformation,[],[f3]) ).
tcf(c_88,plain,
group_element(e_1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_93,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[],[f16]) ).
tcf(c_94,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[],[f13]) ).
tcf(c_95,plain,
product(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_83,c_76]) ).
tcf(c_240,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_239]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_82,c_76]) ).
tcf(c_290,plain,
( ~ product(e_1,e_4,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_289]) ).
tcf(c_310,plain,
! [X0: $i,X1: $i] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_82,c_75]) ).
tcf(c_311,plain,
( ~ product(e_4,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_310]) ).
tcf(c_599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(e_4,e_1)
| ~ product(X3,X2,e_1)
| ~ product(X3,X0,e_4)
| ~ product(X2,e_1,X1)
| ~ product(X0,e_4,X1) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(e_3,e_1)
| ~ product(X3,X2,e_1)
| ~ product(X3,X0,e_3)
| ~ product(X2,e_1,X1)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(e_3,e_4)
| ~ product(X3,X2,e_4)
| ~ product(X3,X0,e_3)
| ~ product(X2,e_4,X1)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_3)
| ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_635,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_3)
| ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_636,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_4)
| ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_642,plain,
! [X0: $i,X1: $i] :
( equalish(e_3,e_4)
| ~ product(X0,e_4,X1)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_659,plain,
product(e_4,e_4,e_4),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_661,plain,
! [X0: $i] :
( product(e_4,X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(e_4)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_662,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| ~ group_element(e_4)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_661]) ).
tcf(c_670,plain,
( equalish(e_1,e_3)
| ~ product(e_3,e_3,e_3)
| ~ product(e_1,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_623]) ).
tcf(c_671,plain,
product(e_3,e_3,e_3),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_789,plain,
! [X0: $i] :
( product(X0,e_3,e_4)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_790,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_789]) ).
tcf(c_867,plain,
( equalish(e_1,e_4)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_636]) ).
tcf(c_885,plain,
! [X0: $i,X1: $i] :
( equalish(e_3,e_4)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_4,X1)
| ~ product(e_4,X0,e_3)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_621]) ).
tcf(c_973,plain,
( equalish(e_1,e_3)
| ~ product(e_4,e_3,e_2)
| ~ product(e_4,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_635]) ).
tcf(c_1032,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(superposition,[status(thm)],[c_74,c_75]) ).
tcf(c_1060,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(superposition,[status(thm)],[c_74,c_76]) ).
tcf(c_1109,plain,
! [X0: $i] :
( equalish(e_4,X0)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_78,c_1032]) ).
tcf(c_1110,plain,
! [X0: $i] :
( equalish(e_4,X0)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1109,c_85]) ).
tcf(c_1171,plain,
( equalish(e_4,e_1)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_1110]) ).
tcf(c_1329,plain,
! [X0: $i] :
( equalish(e_4,X0)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(e_4)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_78,c_1060]) ).
tcf(c_1330,plain,
! [X0: $i] :
( equalish(e_4,X0)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1329,c_85]) ).
tcf(c_1388,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_3) ),
inference(superposition,[status(thm)],[c_1110,c_1060]) ).
tcf(c_1390,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1388,c_93,c_94,c_86]) ).
tcf(c_1577,plain,
! [X0: $i] :
( equalish(e_3,X0)
| product(e_3,e_4,e_1)
| ~ product(X0,e_4,e_2) ),
inference(superposition,[status(thm)],[c_1390,c_75]) ).
tcf(c_1605,plain,
( equalish(e_3,e_1)
| product(e_3,e_4,e_1)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1577]) ).
tcf(c_1679,plain,
! [X0: $i] :
( equalish(e_3,e_4)
| ~ product(X0,e_4,e_2)
| ~ product(X0,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_642]) ).
tcf(c_1684,plain,
( equalish(e_3,e_4)
| ~ product(e_1,e_4,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_1679]) ).
tcf(c_1703,plain,
! [X0: $i] :
( equalish(e_3,e_4)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,X0,e_3)
| ~ product(X0,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_885]) ).
tcf(c_1704,plain,
( equalish(e_3,e_4)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_1,e_3)
| ~ product(e_1,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1703]) ).
tcf(c_2068,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(e_4,e_1)
| ~ product(e_3,e_4,X1)
| ~ product(X2,e_3,e_4)
| ~ product(X2,X0,e_1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_599]) ).
tcf(c_2069,plain,
( equalish(e_4,e_1)
| ~ product(e_3,e_4,e_1)
| ~ product(e_1,e_3,e_4)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_2068]) ).
tcf(c_2441,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(e_3,e_1)
| ~ product(e_4,e_3,X1)
| ~ product(X2,e_4,e_3)
| ~ product(X2,X0,e_1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_601]) ).
tcf(c_2442,plain,
( equalish(e_3,e_1)
| ~ product(e_4,e_3,e_1)
| ~ product(e_1,e_4,e_3)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_2441]) ).
tcf(c_2753,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ group_element(e_3) ),
inference(superposition,[status(thm)],[c_1330,c_1032]) ).
tcf(c_2755,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2753,c_93,c_94,c_86]) ).
tcf(c_3750,plain,
product(e_4,e_3,e_2),
inference(global_subsumption_just,[status(thm)],[c_2755,c_88,c_86,c_94,c_83,c_80,c_79,c_95,c_240,c_290,c_670,c_671,c_790,c_1171,c_1605,c_1684,c_2069,c_2442,c_2755]) ).
tcf(c_3760,plain,
! [X0: $i] :
( equalish(e_4,X0)
| ~ product(X0,e_3,e_2) ),
inference(superposition,[status(thm)],[c_3750,c_75]) ).
tcf(c_3814,plain,
( equalish(e_4,e_1)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_3760]) ).
tcf(c_3815,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3814,c_3750,c_1704,c_973,c_867,c_790,c_671,c_670,c_662,c_659,c_311,c_240,c_95,c_79,c_82,c_83,c_94,c_85,c_86,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-1.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 13:37:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running EPR theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s epr_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 2.74/1.22 % SZS status Started for theBenchmark.p
% 2.74/1.22 % SZS status Unsatisfiable for theBenchmark.p
% 2.74/1.22
% 2.74/1.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.74/1.22
% 2.74/1.22 % ------ iProver source info
% 2.74/1.22
% 2.74/1.22 % git: date: 2026-07-19 20:42:38 +0200
% 2.74/1.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.74/1.22 % git: non_committed_changes: false
% 2.74/1.22
% 2.74/1.22 % ------ Parsing...% successful
% 2.74/1.22
% 2.74/1.22
% 2.74/1.22 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.74/1.22 %
% 2.74/1.22
% 2.74/1.22 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.74/1.22
% 2.74/1.22 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.74/1.22 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.74/1.22 % ------ Proving...
% 2.74/1.22 % ------ Problem Properties
% 2.74/1.22
% 2.74/1.22 %
% 2.74/1.22 % clauses 23
% 2.74/1.22 % conjectures 2
% 2.74/1.22 % EPR 23
% 2.74/1.22 % Horn 22
% 2.74/1.22 % unary 17
% 2.74/1.22 % binary 0
% 2.74/1.22 % lits 42
% 2.74/1.23 % lits eq 0
% 2.74/1.23 % fd_pure 0
% 2.74/1.23 % fd_pseudo 0
% 2.74/1.23 % fd_cond 0
% 2.74/1.23 % fd_pseudo_cond 0
% 2.74/1.23 % AC symbols 0
% 2.74/1.23
% 2.74/1.23 % ------ Schedule EPR non Horn non eq is on
% 2.74/1.23
% 2.74/1.23 % ------ no equalities: superposition off
% 2.74/1.23
% 2.74/1.23 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 2.74/1.23
% 2.74/1.23
% 2.74/1.23 % ------
% 2.74/1.23 % Current options:
% 2.74/1.23 % ------
% 2.74/1.23
% 2.74/1.23
% 2.74/1.23 %
% 2.74/1.23
% 2.74/1.23 % ------ Proving...
% 2.74/1.23 %
% 2.74/1.23
% 2.74/1.23 % SZS status Unsatisfiable for theBenchmark.p
% 2.74/1.23
% 2.74/1.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.74/1.23
% 2.74/1.23
%------------------------------------------------------------------------------