%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP028-1 : TPTP v9.3.1. Released v1.0.0.
% 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 01:29:57 PM UTC 2026
% Result : Unsatisfiable 1.73s 1.29s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 13 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 39 ( 22 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 0 con; 1-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f2,axiom,
! [X0,X1] : product(left_solution(X0,X1),X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_soln) ).
fof(f3,axiom,
! [X0,X1] : product(X0,right_solution(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_soln) ).
fof(f4,negated_conjecture,
! [X0] : ~ product(not_identity(X0),X0,not_identity(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_right_identity) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X2,X5,X4)
| ~ product(X1,X5,X3)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : product(left_solution(X0,X1),X0,X1),
inference(cnf_transformation,[],[f2]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : product(X0,right_solution(X0,X1),X1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,negated_conjecture,
! [X0: $i] : ~ product(not_identity(X0),X0,not_identity(X0)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_57,plain,
product(iProver_bot,right_solution(iProver_bot,iProver_bot),iProver_bot),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_74,negated_conjecture,
! [X0: $i] : ~ product(not_identity(X0),X0,not_identity(X0)),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X1,X4,X3)
| ~ product(X0,X4,X2)
| ~ product(left_solution(X0,X1),X2,X3)
| ~ product(left_solution(X0,X1),X0,X1) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X1,right_solution(X0,X2),X3)
| ~ product(X0,right_solution(X0,X2),X2)
| ~ product(left_solution(X0,X1),X2,X3)
| ~ product(left_solution(X0,X1),X0,X1) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( product(not_identity(right_solution(X0,X1)),right_solution(X0,X1),not_identity(right_solution(X0,X1)))
| ~ product(X0,right_solution(X0,X1),X1)
| ~ product(left_solution(X0,not_identity(right_solution(X0,X1))),X1,not_identity(right_solution(X0,X1)))
| ~ product(left_solution(X0,not_identity(right_solution(X0,X1))),X0,not_identity(right_solution(X0,X1))) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] : ~ product(not_identity(right_solution(X0,X1)),right_solution(X0,X1),not_identity(right_solution(X0,X1))),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_88,plain,
( product(not_identity(right_solution(iProver_bot,iProver_bot)),right_solution(iProver_bot,iProver_bot),not_identity(right_solution(iProver_bot,iProver_bot)))
| ~ product(iProver_bot,right_solution(iProver_bot,iProver_bot),iProver_bot)
| ~ product(left_solution(iProver_bot,not_identity(right_solution(iProver_bot,iProver_bot))),iProver_bot,not_identity(right_solution(iProver_bot,iProver_bot))) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_89,plain,
~ product(not_identity(right_solution(iProver_bot,iProver_bot)),right_solution(iProver_bot,iProver_bot),not_identity(right_solution(iProver_bot,iProver_bot))),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i] : product(left_solution(X0,not_identity(right_solution(X0,X1))),X0,not_identity(right_solution(X0,X1))),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_135,plain,
product(left_solution(iProver_bot,not_identity(right_solution(iProver_bot,iProver_bot))),iProver_bot,not_identity(right_solution(iProver_bot,iProver_bot))),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_136,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_135,c_89,c_88,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP028-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 13:18:13 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_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...
% 1.73/1.29 % SZS status Started for theBenchmark.p
% 1.73/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.73/1.29
% 1.73/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.73/1.29
% 1.73/1.29 % ------ iProver source info
% 1.73/1.29
% 1.73/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.73/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.73/1.29 % git: non_committed_changes: false
% 1.73/1.29
% 1.73/1.29 % ------ Parsing...% successful
% 1.73/1.29
% 1.73/1.29
% 1.73/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.73/1.29
% 1.73/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.73/1.29
% 1.73/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.73/1.29 % ------ Proving...
% 1.73/1.29 % ------ Problem Properties
% 1.73/1.29
% 1.73/1.29 %
% 1.73/1.29 % clauses 4
% 1.73/1.29 % conjectures 1
% 1.73/1.29 % EPR 1
% 1.73/1.29 % Horn 4
% 1.73/1.29 % unary 3
% 1.73/1.29 % binary 0
% 1.73/1.29 % lits 7
% 1.73/1.29 % lits eq 0
% 1.73/1.29 % fd_pure 0
% 1.73/1.29 % fd_pseudo 0
% 1.73/1.29 % fd_cond 0
% 1.73/1.29 % fd_pseudo_cond 0
% 1.73/1.29 % AC symbols 0
% 1.73/1.29
% 1.73/1.29 % ------ Schedule dynamic 5 is on
% 1.73/1.29
% 1.73/1.29 % ------ no equalities: superposition off
% 1.73/1.29
% 1.73/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.73/1.29
% 1.73/1.29
% 1.73/1.29 % ------
% 1.73/1.29 % Current options:
% 1.73/1.29 % ------
% 1.73/1.29
% 1.73/1.29
% 1.73/1.29 %
% 1.73/1.29
% 1.73/1.29 % ------ Proving...
% 1.73/1.29 %
% 1.73/1.29
% 1.73/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.73/1.29
% 1.73/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.73/1.29
% 1.73/1.29
%------------------------------------------------------------------------------