%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP123-7.003 : TPTP v9.3.1. Released v1.2.0.
% 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 01:31:08 PM UTC 2026
% Result : Unsatisfiable 1.31s 16.14s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 19 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 118 ( 60 ~; 58 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 58 ( 0 sgn 58 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f8,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f9,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f10,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f11,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f16,axiom,
! [X0,X1] :
( product1(X0,X1,e_3)
| product1(X0,X1,e_2)
| product1(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function1) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f19,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_left_cancellation) ).
fof(f20,axiom,
! [X0] : product1(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f25,axiom,
! [X0] : product2(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f26,negated_conjecture,
! [X2,X3,X0,X1] :
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1a) ).
tcf(c_75,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_76,plain,
! [X0: $i] : product1(X0,X0,X0),
inference(cnf_transformation,[],[f20]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( product1(X1,X0,e_3)
| product1(X1,X0,e_2)
| product1(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_81,plain,
! [X0: $i] : product2(X0,X0,X0),
inference(cnf_transformation,[],[f25]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_90,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f11]) ).
tcf(c_91,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f10]) ).
tcf(c_92,plain,
group_element(e_3),
inference(cnf_transformation,[],[f9]) ).
tcf(c_93,plain,
group_element(e_2),
inference(cnf_transformation,[],[f8]) ).
tcf(c_94,plain,
group_element(e_1),
inference(cnf_transformation,[],[f7]) ).
tcf(c_96,plain,
product1(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ~ product2(X0,X1,e_2)
| ~ product2(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_91,c_84]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i] :
( ~ product1(X0,e_2,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_91,c_78]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i] :
( ~ product1(e_2,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_91,c_77]) ).
tcf(c_224,plain,
( ~ product1(e_2,e_1,e_1)
| ~ product1(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_223]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i] :
( ~ product1(X0,e_3,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_90,c_78]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i] :
( ~ product1(e_3,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_90,c_77]) ).
tcf(c_272,plain,
( ~ product1(e_3,e_1,e_1)
| ~ product1(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_271]) ).
tcf(c_382,plain,
product2(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_383,plain,
! [X0: $i,X1: $i,X2: $i] :
( product2(X2,e_2,X1)
| ~ product1(e_2,X1,X0)
| ~ product1(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_385,plain,
( ~ product1(e_2,e_2,e_2)
| ~ product1(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_207]) ).
tcf(c_386,plain,
product1(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_396,plain,
( ~ product1(e_3,e_3,e_3)
| ~ product1(e_3,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_255]) ).
tcf(c_397,plain,
product1(e_3,e_3,e_3),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_416,plain,
! [X0: $i] :
( product1(e_2,X0,e_3)
| product1(e_2,X0,e_2)
| product1(e_2,X0,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_418,plain,
( product1(e_2,e_1,e_3)
| product1(e_2,e_1,e_2)
| product1(e_2,e_1,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_416]) ).
tcf(c_423,plain,
! [X0: $i] :
( product1(e_3,X0,e_3)
| product1(e_3,X0,e_2)
| product1(e_3,X0,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_426,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_423]) ).
tcf(c_458,plain,
( ~ product2(e_2,e_2,e_2)
| ~ product2(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_547,plain,
! [X0: $i,X1: $i] :
( product2(X1,e_2,X0)
| ~ product1(e_2,X0,e_3)
| ~ product1(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_383]) ).
tcf(c_648,plain,
! [X0: $i] :
( product2(e_2,e_2,X0)
| ~ product1(e_3,X0,e_2)
| ~ product1(e_2,X0,e_3) ),
inference(instantiation,[status(thm)],[c_547]) ).
tcf(c_649,plain,
( product2(e_2,e_2,e_1)
| ~ product1(e_3,e_1,e_2)
| ~ product1(e_2,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_648]) ).
tcf(c_650,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_649,c_458,c_426,c_418,c_397,c_396,c_386,c_385,c_382,c_272,c_224,c_96,c_92,c_93,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-7.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/15.40 % Computer : n008.cluster.edu
% 0.12/15.40 % Model : x86_64 x86_64
% 0.12/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.40 % Memory : 8046.5625MB
% 0.12/15.40 % OS : Linux 6.8.0-71-generic
% 0.12/15.41 % CPULimit : 300
% 0.12/15.41 % WCLimit : 300
% 0.12/15.41 % DateTime : Wed Sep 23 13:37:40 UTC 2026
% 0.12/15.41 % CPUTime :
% 0.12/15.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/15.45 Running EPR theorem proving
% 0.12/15.45 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s epr_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/15.46
% 0.12/15.46 % ======== iProver multi-core TPTP/SMT =========
% 0.12/15.46
% 0.12/15.46 % Detected problem language: tptp
% 0.12/15.47 % Proving...
% 1.31/16.14 % SZS status Started for theBenchmark.p
% 1.31/16.14 % SZS status Unsatisfiable for theBenchmark.p
% 1.31/16.14
% 1.31/16.14 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.31/16.14
% 1.31/16.14 % ------ iProver source info
% 1.31/16.14
% 1.31/16.14 % git: date: 2026-07-19 20:42:38 +0200
% 1.31/16.14 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.31/16.14 % git: non_committed_changes: false
% 1.31/16.14
% 1.31/16.14 % ------ Parsing...% successful
% 1.31/16.14
% 1.31/16.14
% 1.31/16.14 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.31/16.14 %
% 1.31/16.14
% 1.31/16.14 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e %
% 1.31/16.14
% 1.31/16.14 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.31/16.14 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.31/16.14 % ------ Proving...
% 1.31/16.14 % ------ Problem Properties
% 1.31/16.14
% 1.31/16.14 %
% 1.31/16.14 % clauses 26
% 1.31/16.14 % conjectures 1
% 1.31/16.14 % EPR 26
% 1.31/16.14 % Horn 24
% 1.31/16.14 % unary 5
% 1.31/16.14 % binary 18
% 1.31/16.14 % lits 54
% 1.31/16.14 % lits eq 0
% 1.31/16.14 % fd_pure 0
% 1.31/16.14 % fd_pseudo 0
% 1.31/16.14 % fd_cond 0
% 1.31/16.14 % fd_pseudo_cond 0
% 1.31/16.14 % AC symbols 0
% 1.31/16.14
% 1.31/16.14 % ------ Schedule EPR non Horn non eq is on
% 1.31/16.14
% 1.31/16.14 % ------ no equalities: superposition off
% 1.31/16.14
% 1.31/16.14 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 1.31/16.14
% 1.31/16.14
% 1.31/16.14 % ------
% 1.31/16.14 % Current options:
% 1.31/16.14 % ------
% 1.31/16.14
% 1.31/16.14
% 1.31/16.14 %
% 1.31/16.14
% 1.31/16.14 % ------ Proving...
% 1.31/16.14 %
% 1.31/16.14
% 1.31/16.14 % SZS status Unsatisfiable for theBenchmark.p
% 1.31/16.14
% 1.31/16.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.31/16.15
% 1.31/16.15
%------------------------------------------------------------------------------