%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP004-2 : 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 : n002.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 01:29:52 PM UTC 2026
% Result : Unsatisfiable 0.98s 1.18s
% Output : CNFRefutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 23 unt; 1 def)
% Number of atoms : 101 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 41 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 79 !; 0 ?; 61 :)
% 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(f3,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP005-0.ax',total_function1) ).
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(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,negated_conjecture,
~ product(a,inverse(a),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_right_inverse) ).
tcf(c_57,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_58,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f2]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_60,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,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_63,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_64,negated_conjecture,
~ product(a,inverse(a),identity),
inference(cnf_transformation,[],[f8]) ).
tcf(c_122,definition,
iPr_def_10 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_123,negated_conjecture,
~ product(a,iPr_def_10,identity),
inference(demodulation,[status(thm)],[c_64,c_122]) ).
tcf(c_254,plain,
product(iPr_def_10,a,identity),
inference(superposition,[status(thm)],[c_122,c_58]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ product(identity,X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_60]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(multiply(X0,X1),X2)
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_59,c_60]) ).
tcf(c_278,plain,
! [X0: $i] : equalish(X0,multiply(identity,X0)),
inference(superposition,[status(thm)],[c_59,c_258]) ).
tcf(c_312,plain,
! [X0: $i,X1: $i] :
( product(identity,X0,X1)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_63]) ).
tcf(c_314,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X1,X2)
| ~ equalish(multiply(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_59,c_63]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(identity,X3,X2)
| ~ product(X0,X3,X1)
| ~ product(inverse(X0),X1,X2) ),
inference(superposition,[status(thm)],[c_58,c_62]) ).
tcf(c_336,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(identity,X0,X2)
| ~ product(iPr_def_10,X1,X2)
| ~ product(a,X0,X1) ),
inference(superposition,[status(thm)],[c_254,c_62]) ).
tcf(c_352,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(a,iPr_def_10,identity)
| ~ product(X1,iPr_def_10,X2)
| ~ product(X0,X2,identity)
| ~ product(X0,X1,a) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_357,plain,
product(a,iPr_def_10,multiply(a,iPr_def_10)),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X1)
| ~ equalish(X0,X2)
| ~ product(identity,X0,X1) ),
inference(superposition,[status(thm)],[c_312,c_60]) ).
tcf(c_469,plain,
! [X0: $i,X1: $i] : product(X0,X1,multiply(identity,multiply(X0,X1))),
inference(superposition,[status(thm)],[c_278,c_314]) ).
tcf(c_475,plain,
! [X0: $i] : equalish(X0,multiply(identity,multiply(identity,X0))),
inference(superposition,[status(thm)],[c_469,c_258]) ).
tcf(c_507,plain,
! [X0: $i] :
( product(a,iPr_def_10,identity)
| ~ product(identity,a,a)
| ~ product(identity,X0,identity)
| ~ product(a,iPr_def_10,X0) ),
inference(instantiation,[status(thm)],[c_352]) ).
tcf(c_508,plain,
product(identity,a,a),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_609,plain,
( product(a,iPr_def_10,identity)
| ~ product(identity,a,a)
| ~ product(identity,multiply(a,iPr_def_10),identity)
| ~ product(a,iPr_def_10,multiply(a,iPr_def_10)) ),
inference(instantiation,[status(thm)],[c_507]) ).
tcf(c_1945,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_375]) ).
tcf(c_2033,plain,
! [X0: $i] : equalish(multiply(identity,multiply(identity,X0)),X0),
inference(superposition,[status(thm)],[c_475,c_1945]) ).
tcf(c_2385,plain,
! [X0: $i] : product(identity,multiply(identity,X0),X0),
inference(superposition,[status(thm)],[c_2033,c_314]) ).
tcf(c_2398,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(multiply(identity,X0),X1) ),
inference(superposition,[status(thm)],[c_2385,c_375]) ).
tcf(c_2995,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ product(identity,X0,X1) ),
inference(superposition,[status(thm)],[c_260,c_2398]) ).
tcf(c_3232,plain,
! [X0: $i,X1: $i] :
( product(identity,X1,identity)
| ~ product(X0,X1,X0) ),
inference(superposition,[status(thm)],[c_58,c_334]) ).
tcf(c_5295,plain,
! [X0: $i,X1: $i] :
( product(identity,X0,X1)
| ~ product(iPr_def_10,multiply(a,X0),X1) ),
inference(superposition,[status(thm)],[c_59,c_336]) ).
tcf(c_5308,plain,
! [X0: $i] : product(identity,X0,multiply(iPr_def_10,multiply(a,X0))),
inference(superposition,[status(thm)],[c_59,c_5295]) ).
tcf(c_5353,plain,
! [X0: $i] : equalish(multiply(iPr_def_10,multiply(a,X0)),X0),
inference(superposition,[status(thm)],[c_5308,c_2995]) ).
tcf(c_5477,plain,
! [X0: $i] : product(iPr_def_10,multiply(a,X0),X0),
inference(superposition,[status(thm)],[c_5353,c_314]) ).
tcf(c_5503,plain,
product(identity,multiply(a,iPr_def_10),identity),
inference(superposition,[status(thm)],[c_5477,c_3232]) ).
tcf(c_5518,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5503,c_609,c_508,c_357,c_123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n002.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 13:14:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 0.98/1.18 % SZS status Started for theBenchmark.p
% 0.98/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 0.98/1.18
% 0.98/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.98/1.18
% 0.98/1.18 % ------ iProver source info
% 0.98/1.18
% 0.98/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 0.98/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.98/1.18 % git: non_committed_changes: false
% 0.98/1.18
% 0.98/1.18 % ------ Parsing...% successful
% 0.98/1.18
% 0.98/1.18
% 0.98/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.98/1.18
% 0.98/1.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.98/1.18
% 0.98/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.98/1.18
% 0.98/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.98/1.18 % ------ Proving...
% 0.98/1.18 % ------ Problem Properties
% 0.98/1.18
% 0.98/1.18 %
% 0.98/1.18 % clauses 9
% 0.98/1.18 % conjectures 1
% 0.98/1.18 % EPR 6
% 0.98/1.18 % Horn 9
% 0.98/1.18 % unary 5
% 0.98/1.18 % binary 0
% 0.98/1.18 % lits 19
% 0.98/1.18 % lits eq 1
% 0.98/1.18 % fd_pure 0
% 0.98/1.18 % fd_pseudo 0
% 0.98/1.18 % fd_cond 0
% 0.98/1.18 % fd_pseudo_cond 0
% 0.98/1.18 % AC symbols 0
% 0.98/1.18
% 0.98/1.18 % ------ Schedule dynamic 5 is on
% 0.98/1.18
% 0.98/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.98/1.18
% 0.98/1.18
% 0.98/1.18 % ------
% 0.98/1.18 % Current options:
% 0.98/1.18 % ------
% 0.98/1.18
% 0.98/1.18
% 0.98/1.18 %
% 0.98/1.18
% 0.98/1.18 % ------ Proving...
% 0.98/1.18 %
% 0.98/1.18
% 0.98/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 0.98/1.18
% 0.98/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.98/1.18
% 0.98/1.18
%------------------------------------------------------------------------------