%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP123-1.003 : 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 : n016.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 01:31:07 PM UTC 2026
% Result : Unsatisfiable 0.69s 1.12s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 19 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 102 ( 50 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 50 ( 0 sgn 50 !; 0 ?; 33 :)
% 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(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f8,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f9,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f10,axiom,
! [X0,X1] :
( 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(f12,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(f13,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(f14,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f16,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X1,X4)
| ~ product(X5,X4,X3)
| ~ product(X5,X1,X0)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_2) ).
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_67,plain,
group_element(e_3),
inference(cnf_transformation,[],[f3]) ).
tcf(c_69,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_71,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[],[f7]) ).
tcf(c_72,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[],[f8]) ).
tcf(c_73,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[],[f9]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f10]) ).
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,[],[f12]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_78,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f14]) ).
tcf(c_80,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equalish(X1,X4)
| ~ product(X5,X4,X3)
| ~ product(X5,X1,X0)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_81,plain,
product(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X1)
| ~ product(X3,X2,X2)
| ~ product(X3,X1,X0)
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_78,c_80]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(superposition,[status(thm)],[c_78,c_76]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(superposition,[status(thm)],[c_78,c_77]) ).
tcf(c_136,plain,
! [X0: $i] :
( equalish(e_3,X0)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_74,c_118]) ).
tcf(c_137,plain,
! [X0: $i] :
( equalish(e_3,X0)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_136,c_67]) ).
tcf(c_140,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_137]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(e_1,e_3)
| ~ product(X3,e_3,X2)
| ~ product(X3,e_1,X0)
| ~ product(X2,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_170,plain,
( equalish(e_1,e_3)
| ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_169]) ).
tcf(c_239,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_3)
| product(e_2,e_3,e_1)
| ~ group_element(e_2) ),
inference(superposition,[status(thm)],[c_137,c_101]) ).
tcf(c_240,plain,
product(e_2,e_3,e_1),
inference(forward_subsumption_resolution,[status(thm)],[c_239,c_73,c_71,c_66]) ).
tcf(c_329,plain,
! [X0: $i] :
( equalish(e_1,e_3)
| ~ product(X0,e_3,e_2)
| ~ product(X0,e_1,e_1) ),
inference(superposition,[status(thm)],[c_240,c_88]) ).
tcf(c_334,plain,
! [X0: $i] :
( ~ product(X0,e_3,e_2)
| ~ product(X0,e_1,e_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_329,c_69]) ).
tcf(c_339,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_334]) ).
tcf(c_340,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_339,c_170,c_140,c_69,c_72,c_81,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n016.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 13:39:40 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running EPR theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 0.69/1.12 % SZS status Started for theBenchmark.p
% 0.69/1.12 % SZS status Unsatisfiable for theBenchmark.p
% 0.69/1.12
% 0.69/1.12 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.69/1.12
% 0.69/1.12 % ------ iProver source info
% 0.69/1.12
% 0.69/1.12 % git: date: 2026-07-19 20:42:38 +0200
% 0.69/1.12 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.69/1.12 % git: non_committed_changes: false
% 0.69/1.12
% 0.69/1.12 % ------ Parsing...% successful
% 0.69/1.12
% 0.69/1.12
% 0.69/1.12 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.69/1.12 % ------ Proving...
% 0.69/1.12 % ------ Problem Properties
% 0.69/1.12
% 0.69/1.12 %
% 0.69/1.12 % clauses 16
% 0.69/1.12 % conjectures 2
% 0.69/1.12 % EPR 16
% 0.69/1.12 % Horn 15
% 0.69/1.12 % unary 10
% 0.69/1.12 % binary 0
% 0.69/1.12 % lits 34
% 0.69/1.12 % lits eq 0
% 0.69/1.12 % fd_pure 0
% 0.69/1.12 % fd_pseudo 0
% 0.69/1.12 % fd_cond 0
% 0.69/1.12 % fd_pseudo_cond 0
% 0.69/1.12 % AC symbols 0
% 0.69/1.13
% 0.69/1.13 % ------ Input Options Time Limit: Unbounded
% 0.69/1.13
% 0.69/1.13
% 0.69/1.13 % ------
% 0.69/1.13 % Current options:
% 0.69/1.13 % ------
% 0.69/1.13
% 0.69/1.13
% 0.69/1.13 %
% 0.69/1.13
% 0.69/1.13 % ------ Proving...
% 0.69/1.13 %
% 0.69/1.13
% 0.69/1.13 % SZS status Unsatisfiable for theBenchmark.p
% 0.69/1.13
% 0.69/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.69/1.13
% 0.69/1.13
%------------------------------------------------------------------------------