%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP048-2 : 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 : 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 01:30:02 PM UTC 2026
% Result : Unsatisfiable 10.59s 8.01s
% Output : CNFRefutation 10.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 20 unt; 0 def)
% Number of atoms : 142 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 176 ( 89 ~; 87 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 98 ( 0 sgn 98 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',left_inverse) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',total_function2) ).
fof(f5,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',associativity1) ).
fof(f6,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/Axioms/GRP005-0.ax',associativity2) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).
fof(f8,axiom,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b) ).
fof(f9,negated_conjecture,
~ equalish(inverse(a),inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_substitution) ).
tcf(c_58,plain,
equalish(a,b),
inference(cnf_transformation,[],[f8]) ).
tcf(c_59,negated_conjecture,
~ equalish(inverse(a),inverse(b)),
inference(cnf_transformation,[],[f9]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X1,X3)
| ~ equalish(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_62,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f2]) ).
tcf(c_63,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,[],[f6]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_65,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
product(identity,a,a),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_67,plain,
product(inverse(a),a,identity),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ product(identity,X0,X1)
| ~ product(identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_146,plain,
( equalish(a,a)
| ~ product(identity,a,a) ),
inference(instantiation,[status(thm)],[c_145]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(inverse(X0),X2,X3)
| ~ product(identity,X1,X3)
| ~ product(X0,X1,X2)
| ~ product(inverse(X0),X0,identity) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( product(inverse(inverse(X0)),identity,X1)
| ~ product(identity,X0,X1)
| ~ product(inverse(X0),X0,identity)
| ~ product(inverse(inverse(X0)),inverse(X0),identity) ),
inference(instantiation,[status(thm)],[c_150]) ).
tcf(c_164,plain,
( product(inverse(inverse(a)),identity,a)
| ~ product(identity,a,a)
| ~ product(inverse(a),a,identity)
| ~ product(inverse(inverse(a)),inverse(a),identity) ),
inference(instantiation,[status(thm)],[c_163]) ).
tcf(c_166,plain,
( equalish(inverse(a),inverse(b))
| ~ product(identity,inverse(a),inverse(b))
| ~ product(identity,inverse(a),inverse(a)) ),
inference(instantiation,[status(thm)],[c_145]) ).
tcf(c_182,plain,
product(identity,inverse(a),inverse(a)),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_239,plain,
! [X0: $i] : product(inverse(inverse(X0)),inverse(X0),identity),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_240,plain,
product(inverse(inverse(a)),inverse(a),identity),
inference(instantiation,[status(thm)],[c_239]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i] :
( product(identity,X0,X1)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_65,c_60]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(identity,X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_257,c_60]) ).
tcf(c_399,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X1)
| ~ equalish(X0,X2)
| ~ product(identity,X0,X1) ),
inference(superposition,[status(thm)],[c_257,c_61]) ).
tcf(c_658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(inverse(inverse(X0)),X4,X3)
| ~ product(identity,X2,X4)
| ~ product(X1,X2,X3)
| ~ product(inverse(inverse(X0)),identity,X1) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X3,X4,X2)
| ~ product(identity,X4,X1)
| ~ product(inverse(inverse(X0)),identity,X3)
| ~ product(inverse(inverse(X0)),X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1038,plain,
product(identity,inverse(b),inverse(b)),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_65,c_399]) ).
tcf(c_1210,plain,
! [X0: $i] :
( product(inverse(inverse(X0)),identity,inverse(b))
| ~ product(identity,X0,inverse(b))
| ~ product(inverse(X0),X0,identity)
| ~ product(inverse(inverse(X0)),inverse(X0),identity) ),
inference(instantiation,[status(thm)],[c_163]) ).
tcf(c_1230,plain,
equalish(b,a),
inference(superposition,[status(thm)],[c_58,c_1153]) ).
tcf(c_1260,plain,
! [X0: $i] :
( product(identity,b,X0)
| ~ equalish(a,X0) ),
inference(superposition,[status(thm)],[c_1230,c_294]) ).
tcf(c_1264,plain,
( product(identity,b,a)
| ~ equalish(a,a) ),
inference(instantiation,[status(thm)],[c_1260]) ).
tcf(c_2088,plain,
! [X0: $i] : product(inverse(inverse(inverse(X0))),inverse(inverse(X0)),identity),
inference(instantiation,[status(thm)],[c_239]) ).
tcf(c_2200,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(inverse(inverse(X0)),X2,identity)
| ~ product(identity,X1,X2)
| ~ product(inverse(X1),X1,identity)
| ~ product(inverse(inverse(X0)),identity,inverse(X1)) ),
inference(instantiation,[status(thm)],[c_658]) ).
tcf(c_2232,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X2,identity)
| ~ product(identity,X2,inverse(X0))
| ~ product(inverse(inverse(X0)),identity,X1)
| ~ product(inverse(inverse(X0)),inverse(X0),identity) ),
inference(instantiation,[status(thm)],[c_659]) ).
tcf(c_3227,plain,
( product(inverse(inverse(inverse(b))),identity,inverse(b))
| ~ product(identity,inverse(b),inverse(b))
| ~ product(inverse(inverse(b)),inverse(b),identity)
| ~ product(inverse(inverse(inverse(b))),inverse(inverse(b)),identity) ),
inference(instantiation,[status(thm)],[c_1210]) ).
tcf(c_3247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(identity,X4,X2)
| ~ product(X3,X4,X1)
| ~ product(inverse(inverse(inverse(X0))),X3,identity)
| ~ product(inverse(inverse(inverse(X0))),X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_5564,plain,
! [X0: $i,X1: $i] :
( product(X1,inverse(X0),identity)
| ~ product(identity,inverse(X0),inverse(X0))
| ~ product(inverse(inverse(X0)),identity,X1)
| ~ product(inverse(inverse(X0)),inverse(X0),identity) ),
inference(instantiation,[status(thm)],[c_2232]) ).
tcf(c_5566,plain,
( product(a,inverse(a),identity)
| ~ product(identity,inverse(a),inverse(a))
| ~ product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),inverse(a),identity) ),
inference(instantiation,[status(thm)],[c_5564]) ).
tcf(c_8404,plain,
product(inverse(inverse(b)),inverse(b),identity),
inference(instantiation,[status(thm)],[c_239]) ).
tcf(c_10970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(identity,inverse(a),X2)
| ~ product(X3,inverse(a),X1)
| ~ product(inverse(inverse(inverse(X0))),X3,identity)
| ~ product(inverse(inverse(inverse(X0))),X1,X2) ),
inference(instantiation,[status(thm)],[c_3247]) ).
tcf(c_15733,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(identity,inverse(a),X2)
| ~ product(X1,inverse(a),identity)
| ~ product(inverse(inverse(inverse(X0))),identity,X2)
| ~ product(inverse(inverse(inverse(X0))),X1,identity) ),
inference(instantiation,[status(thm)],[c_10970]) ).
tcf(c_28702,plain,
product(inverse(inverse(inverse(b))),inverse(inverse(b)),identity),
inference(instantiation,[status(thm)],[c_2088]) ).
tcf(c_37469,plain,
! [X0: $i] :
( product(inverse(inverse(inverse(b))),X0,identity)
| ~ product(identity,b,X0)
| ~ product(inverse(b),b,identity)
| ~ product(inverse(inverse(inverse(b))),identity,inverse(b)) ),
inference(instantiation,[status(thm)],[c_2200]) ).
tcf(c_37470,plain,
( product(inverse(inverse(inverse(b))),a,identity)
| ~ product(identity,b,a)
| ~ product(inverse(b),b,identity)
| ~ product(inverse(inverse(inverse(b))),identity,inverse(b)) ),
inference(instantiation,[status(thm)],[c_37469]) ).
tcf(c_37474,plain,
! [X0: $i] :
( product(identity,inverse(a),inverse(b))
| ~ product(X0,inverse(a),identity)
| ~ product(inverse(inverse(inverse(b))),X0,identity)
| ~ product(inverse(inverse(inverse(b))),identity,inverse(b)) ),
inference(instantiation,[status(thm)],[c_15733]) ).
tcf(c_37477,plain,
( product(identity,inverse(a),inverse(b))
| ~ product(a,inverse(a),identity)
| ~ product(inverse(inverse(inverse(b))),a,identity)
| ~ product(inverse(inverse(inverse(b))),identity,inverse(b)) ),
inference(instantiation,[status(thm)],[c_37474]) ).
tcf(c_51624,plain,
product(inverse(b),b,identity),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_51625,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_51624,c_37477,c_37470,c_28702,c_8404,c_5566,c_3227,c_1264,c_1038,c_240,c_182,c_166,c_164,c_146,c_59,c_67,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP048-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.58 % Computer : n016.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.59 % CPULimit : 300
% 0.10/5.59 % WCLimit : 300
% 0.10/5.59 % DateTime : Wed Sep 23 13:28:33 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.10/5.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.62 Running first-order theorem proving
% 0.14/5.62 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
% 0.14/5.63
% 0.14/5.63 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.63
% 0.14/5.63 % Detected problem language: tptp
% 0.14/5.65 % Proving...
% 10.59/8.01 % SZS status Started for theBenchmark.p
% 10.59/8.01 % SZS status Unsatisfiable for theBenchmark.p
% 10.59/8.01
% 10.59/8.01 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.59/8.01
% 10.59/8.01 % ------ iProver source info
% 10.59/8.01
% 10.59/8.01 % git: date: 2026-07-19 20:42:38 +0200
% 10.59/8.01 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.59/8.01 % git: non_committed_changes: false
% 10.59/8.01
% 10.59/8.01 % ------ Parsing...% successful
% 10.59/8.01
% 10.59/8.01
% 10.59/8.01 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.59/8.01
% 10.59/8.01 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.59/8.01
% 10.59/8.01 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 10.59/8.01 % ------ Proving...
% 10.59/8.01 % ------ Problem Properties
% 10.59/8.01
% 10.59/8.01 %
% 10.59/8.01 % clauses 8
% 10.59/8.01 % conjectures 1
% 10.59/8.01 % EPR 6
% 10.59/8.01 % Horn 8
% 10.59/8.01 % unary 4
% 10.59/8.01 % binary 0
% 10.59/8.01 % lits 18
% 10.59/8.01 % lits eq 0
% 10.59/8.01 % fd_pure 0
% 10.59/8.01 % fd_pseudo 0
% 10.59/8.01 % fd_cond 0
% 10.59/8.01 % fd_pseudo_cond 0
% 10.59/8.01 % AC symbols 0
% 10.59/8.01
% 10.59/8.01 % ------ Schedule dynamic 5 is on
% 10.59/8.01
% 10.59/8.01 % ------ no equalities: superposition off
% 10.59/8.01
% 10.59/8.01 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.59/8.01
% 10.59/8.01
% 10.59/8.01 % ------
% 10.59/8.01 % Current options:
% 10.59/8.01 % ------
% 10.59/8.01
% 10.59/8.01
% 10.59/8.01 %
% 10.59/8.01
% 10.59/8.01 % ------ Proving...
% 10.59/8.01 %
% 10.59/8.01
% 10.59/8.01 % SZS status Unsatisfiable for theBenchmark.p
% 10.59/8.01
% 10.59/8.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.59/8.01
% 10.59/8.01
%------------------------------------------------------------------------------