%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP036-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 01:29:59 PM UTC 2026
% Result : Unsatisfiable 0.59s 6.29s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 17 unt; 0 def)
% Number of atoms : 51 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 27 ( 15 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
fof(f8,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/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity2) ).
fof(f10,axiom,
! [X0] :
( product(another_identity,X0,X0)
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_left_identity) ).
fof(f15,axiom,
subgroup_member(another_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_identity_in_subgroup) ).
fof(f16,negated_conjecture,
identity != another_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_identity_equals_another_identity) ).
tcf(c_66,plain,
! [X0: $i] : product(X0,identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f4]) ).
tcf(c_72,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,[],[f8]) ).
tcf(c_74,plain,
! [X0: $i] :
( product(another_identity,X0,X0)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_79,plain,
subgroup_member(another_identity),
inference(cnf_transformation,[],[f15]) ).
tcf(c_80,negated_conjecture,
another_identity != identity,
inference(cnf_transformation,[],[f16]) ).
tcf(c_91,plain,
! [X0: $i] :
( ( multiply(another_identity,X0) = X0 )
| ~ subgroup_member(X0) ),
inference(well_definedness,[status(thm)],[c_74]) ).
tcf(c_98,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(well_definedness,[status(thm)],[c_66]) ).
tcf(c_100,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(well_definedness,[status(thm)],[c_68]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( multiply(X2,X5) = X4 )
| ( multiply(X1,X5) != X3 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_72]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_106]) ).
tcf(c_285,negated_conjecture,
another_identity != identity,
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_444,plain,
multiply(another_identity,another_identity) = another_identity,
inference(superposition,[status(thm)],[c_79,c_91]) ).
tcf(c_448,plain,
! [X0: $i] : multiply(another_identity,multiply(another_identity,X0)) = multiply(another_identity,X0),
inference(superposition,[status(thm)],[c_444,c_207]) ).
tcf(c_484,plain,
multiply(another_identity,identity) = identity,
inference(superposition,[status(thm)],[c_100,c_448]) ).
tcf(c_488,plain,
another_identity = identity,
inference(demodulation,[status(thm)],[c_484,c_98]) ).
tcf(c_489,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_488,c_285]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP036-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/5.53 % Computer : n012.cluster.edu
% 0.03/5.53 % Model : x86_64 x86_64
% 0.03/5.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.53 % Memory : 8046.5625MB
% 0.03/5.53 % OS : Linux 6.8.0-71-generic
% 0.03/5.53 % CPULimit : 300
% 0.03/5.53 % WCLimit : 300
% 0.03/5.53 % DateTime : Wed Sep 23 13:20:00 UTC 2026
% 0.03/5.53 % CPUTime :
% 0.03/5.53 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/5.55 Running first-order theorem proving
% 0.03/5.55 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/5.55
% 0.03/5.55 % ======== iProver multi-core TPTP/SMT =========
% 0.03/5.55
% 0.03/5.55 % Detected problem language: tptp
% 0.03/5.56 % Proving...
% 0.59/6.29 % SZS status Started for theBenchmark.p
% 0.59/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.59/6.29
% 0.59/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.59/6.29
% 0.59/6.29 % ------ iProver source info
% 0.59/6.29
% 0.59/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.59/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.59/6.29 % git: non_committed_changes: false
% 0.59/6.29
% 0.59/6.29 % ------ Parsing...% successful
% 0.59/6.29
% 0.59/6.29
% 0.59/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.59/6.29
% 0.59/6.29 % ------ Preprocessing... sup_sim: 5 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.59/6.29
% 0.59/6.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.59/6.29
% 0.59/6.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.59/6.29 % ------ Proving...
% 0.59/6.29 % ------ Problem Properties
% 0.59/6.29
% 0.59/6.29 %
% 0.59/6.29 % clauses 13
% 0.59/6.29 % conjectures 1
% 0.59/6.29 % EPR 2
% 0.59/6.29 % Horn 13
% 0.59/6.29 % unary 7
% 0.59/6.29 % binary 5
% 0.59/6.29 % lits 20
% 0.59/6.29 % lits eq 10
% 0.59/6.29 % fd_pure 0
% 0.59/6.29 % fd_pseudo 0
% 0.59/6.29 % fd_cond 0
% 0.59/6.29 % fd_pseudo_cond 0
% 0.59/6.29 % AC symbols 0
% 0.59/6.29
% 0.59/6.29 % ------ Schedule dynamic 5 is on
% 0.59/6.29
% 0.59/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.59/6.29
% 0.59/6.29
% 0.59/6.29 % ------
% 0.59/6.29 % Current options:
% 0.59/6.29 % ------
% 0.59/6.29
% 0.59/6.29
% 0.59/6.29 %
% 0.59/6.29
% 0.59/6.29 % ------ Proving...
% 0.59/6.29 %
% 0.59/6.29
% 0.59/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.59/6.29
% 0.59/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.59/6.29
% 0.59/6.29
%------------------------------------------------------------------------------