%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP135-1.002 : 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 : n018.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 01:31:32 PM UTC 2026
% Result : Unsatisfiable 1.85s 1.22s
% Output : CNFRefutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 7 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 100 ( 50 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f3,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f5,axiom,
! [X0,X1] :
( product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f9,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
tcf(c_58,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_63,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f3]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_65,plain,
group_element(e_1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
group_element(e_2),
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_63,c_60]) ).
tcf(c_118,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_63,c_59]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X0,X1)
| ~ product(X2,X0,e_2)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_176,plain,
! [X0: $i] :
( product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_178,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_176]) ).
tcf(c_179,plain,
! [X0: $i] :
( product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_181,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_179]) ).
tcf(c_197,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_176]) ).
tcf(c_198,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i] :
( product(e_2,e_2,X0)
| ~ product(X1,e_2,e_2)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_175]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X0,X1)
| ~ product(e_2,X0,X2)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_208,plain,
( product(e_1,e_1,e_1)
| ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_207]) ).
tcf(c_227,plain,
! [X0: $i] :
( ~ product(e_2,X0,e_2)
| ~ product(e_1,X0,e_2) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_229,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_227]) ).
tcf(c_251,plain,
( product(e_2,e_2,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_202]) ).
tcf(c_400,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_251,c_229,c_208,c_198,c_197,c_181,c_178,c_118,c_68,c_65,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP135-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n018.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 : Wed Sep 23 13:51:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running EPR theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.85/1.22 % SZS status Started for theBenchmark.p
% 1.85/1.22 % SZS status Unsatisfiable for theBenchmark.p
% 1.85/1.22
% 1.85/1.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.85/1.22
% 1.85/1.22 % ------ iProver source info
% 1.85/1.22
% 1.85/1.22 % git: date: 2026-07-19 20:42:38 +0200
% 1.85/1.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.85/1.22 % git: non_committed_changes: false
% 1.85/1.22
% 1.85/1.22 % ------ Parsing...% successful
% 1.85/1.22
% 1.85/1.22
% 1.85/1.22 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.85/1.22 %
% 1.85/1.22
% 1.85/1.22 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.85/1.22
% 1.85/1.22 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.85/1.22 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.85/1.22 % ------ Proving...
% 1.85/1.22 % ------ Problem Properties
% 1.85/1.22
% 1.85/1.22 %
% 1.85/1.22 % clauses 7
% 1.85/1.22 % conjectures 1
% 1.85/1.22 % EPR 7
% 1.85/1.22 % Horn 6
% 1.85/1.22 % unary 2
% 1.85/1.22 % binary 3
% 1.85/1.22 % lits 15
% 1.85/1.22 % lits eq 0
% 1.85/1.22 % fd_pure 0
% 1.85/1.22 % fd_pseudo 0
% 1.85/1.22 % fd_cond 0
% 1.85/1.22 % fd_pseudo_cond 0
% 1.85/1.22 % AC symbols 0
% 1.85/1.22
% 1.85/1.22 % ------ Schedule EPR non Horn non eq is on
% 1.85/1.22
% 1.85/1.22 % ------ no equalities: superposition off
% 1.85/1.22
% 1.85/1.22 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 1.85/1.22
% 1.85/1.22
% 1.85/1.22 % ------
% 1.85/1.22 % Current options:
% 1.85/1.22 % ------
% 1.85/1.22
% 1.85/1.22
% 1.85/1.22 %
% 1.85/1.22
% 1.85/1.22 % ------ Proving...
% 1.85/1.22 %
% 1.85/1.22
% 1.85/1.22 % SZS status Unsatisfiable for theBenchmark.p
% 1.85/1.22
% 1.85/1.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.85/1.22
% 1.85/1.22
%------------------------------------------------------------------------------