%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP123-6.003 : 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 : n011.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 1.91s 1.21s
% Output : CNFRefutation 1.91s
% 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(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f4,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f10,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/sandbox/benchmark/theBenchmark.p',product1_total_function1) ).
fof(f12,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_left_cancellation) ).
fof(f14,axiom,
! [X0] : product1(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f19,axiom,
! [X0] : product2(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f20,negated_conjecture,
! [X2,X3,X0,X1] :
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1a) ).
tcf(c_69,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,[],[f20]) ).
tcf(c_70,plain,
! [X0: $i] : product1(X0,X0,X0),
inference(cnf_transformation,[],[f14]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( product1(X0,X1,e_3)
| product1(X0,X1,e_2)
| product1(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_75,plain,
! [X0: $i] : product2(X0,X0,X0),
inference(cnf_transformation,[],[f19]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_82,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_83,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f4]) ).
tcf(c_84,plain,
group_element(e_1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_85,plain,
group_element(e_3),
inference(cnf_transformation,[],[f3]) ).
tcf(c_86,plain,
group_element(e_2),
inference(cnf_transformation,[],[f2]) ).
tcf(c_90,plain,
product1(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i] :
( ~ product2(X0,X1,e_2)
| ~ product2(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_83,c_78]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] :
( ~ product1(X0,e_2,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_83,c_72]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i] :
( ~ product1(e_2,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_83,c_71]) ).
tcf(c_218,plain,
( ~ product1(e_2,e_1,e_1)
| ~ product1(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_217]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] :
( ~ product1(X0,e_3,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_82,c_72]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] :
( ~ product1(e_3,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_82,c_71]) ).
tcf(c_266,plain,
( ~ product1(e_3,e_1,e_1)
| ~ product1(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_265]) ).
tcf(c_375,plain,
( ~ product2(e_2,e_2,e_2)
| ~ product2(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_177]) ).
tcf(c_376,plain,
product2(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_380,plain,
product1(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i,X2: $i] :
( product2(e_2,X0,X1)
| ~ product1(X2,X1,e_2)
| ~ product1(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_397,plain,
product1(e_3,e_3,e_3),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_427,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_74]) ).
tcf(c_429,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_427]) ).
tcf(c_434,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_74]) ).
tcf(c_437,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_434]) ).
tcf(c_479,plain,
( ~ product1(e_2,e_2,e_2)
| ~ product1(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_201]) ).
tcf(c_497,plain,
( ~ product1(e_3,e_3,e_3)
| ~ product1(e_3,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_249]) ).
tcf(c_569,plain,
! [X0: $i,X1: $i] :
( product2(e_2,X0,X1)
| ~ product1(e_3,X1,e_2)
| ~ product1(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_389]) ).
tcf(c_691,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_569]) ).
tcf(c_696,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_691]) ).
tcf(c_697,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_696,c_497,c_479,c_437,c_429,c_397,c_380,c_376,c_375,c_266,c_218,c_90,c_84,c_85,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP123-6.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 13:36:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running EPR theorem proving
% 0.12/0.39 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 1.91/1.21 % SZS status Started for theBenchmark.p
% 1.91/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 1.91/1.21
% 1.91/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.91/1.21
% 1.91/1.21 % ------ iProver source info
% 1.91/1.21
% 1.91/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 1.91/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.91/1.21 % git: non_committed_changes: false
% 1.91/1.21
% 1.91/1.21 % ------ Parsing...% successful
% 1.91/1.21
% 1.91/1.21
% 1.91/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.91/1.21 %
% 1.91/1.21
% 1.91/1.21 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e %
% 1.91/1.21
% 1.91/1.21 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.91/1.21 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.91/1.21 % ------ Proving...
% 1.91/1.21 % ------ Problem Properties
% 1.91/1.21
% 1.91/1.21 %
% 1.91/1.21 % clauses 26
% 1.91/1.21 % conjectures 1
% 1.91/1.21 % EPR 26
% 1.91/1.21 % Horn 24
% 1.91/1.21 % unary 5
% 1.91/1.21 % binary 18
% 1.91/1.21 % lits 54
% 1.91/1.21 % lits eq 0
% 1.91/1.21 % fd_pure 0
% 1.91/1.21 % fd_pseudo 0
% 1.91/1.21 % fd_cond 0
% 1.91/1.21 % fd_pseudo_cond 0
% 1.91/1.21 % AC symbols 0
% 1.91/1.21
% 1.91/1.21 % ------ Schedule EPR non Horn non eq is on
% 1.91/1.21
% 1.91/1.21 % ------ no equalities: superposition off
% 1.91/1.21
% 1.91/1.21 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 1.91/1.21
% 1.91/1.21
% 1.91/1.21 % ------
% 1.91/1.21 % Current options:
% 1.91/1.21 % ------
% 1.91/1.21
% 1.91/1.21
% 1.91/1.21 %
% 1.91/1.21
% 1.91/1.21 % ------ Proving...
% 1.91/1.21 %
% 1.91/1.21
% 1.91/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 1.91/1.21
% 1.91/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.91/1.21
% 1.91/1.21
%------------------------------------------------------------------------------