%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP047-2 : 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 5.92s 2.28s
% Output : CNFRefutation 5.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 23 unt; 0 def)
% Number of atoms : 139 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 161 ( 82 ~; 79 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 106 !; 0 ?; 82 :)
% 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(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(multiply(c,a),multiply(c,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_substitution2) ).
tcf(c_58,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_59,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f2]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
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,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_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] :
( product(X0,X1,X3)
| ~ equalish(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_65,plain,
equalish(a,b),
inference(cnf_transformation,[],[f8]) ).
tcf(c_66,negated_conjecture,
~ equalish(multiply(c,a),multiply(c,b)),
inference(cnf_transformation,[],[f9]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X3,X4,multiply(c,b))
| ~ product(X2,X4,X1)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,multiply(c,b)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_164,plain,
product(identity,multiply(c,b),multiply(c,b)),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_165,plain,
product(c,b,multiply(c,b)),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X2,X1)
| ~ product(identity,X1,X1)
| ~ product(X3,X0,identity)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X2,X4,multiply(X0,X1))
| ~ product(X3,X1,X4)
| ~ product(X2,X3,X0)
| ~ product(X0,X1,multiply(X0,X1)) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ product(identity,X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_61]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(multiply(X0,X1),X2)
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_60,c_61]) ).
tcf(c_248,plain,
! [X0: $i] : equalish(X0,multiply(identity,X0)),
inference(superposition,[status(thm)],[c_60,c_225]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i] :
( product(identity,X0,X1)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_64]) ).
tcf(c_270,plain,
! [X0: $i] : product(inverse(inverse(X0)),inverse(X0),identity),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_305,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(inverse(X0),X2,X1)
| ~ product(identity,X1,X1)
| ~ product(X0,X1,X2)
| ~ product(inverse(X0),X0,identity) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_314,plain,
! [X0: $i,X1: $i] :
( product(X1,multiply(c,b),multiply(X0,b))
| ~ product(X1,c,X0)
| ~ product(c,b,multiply(c,b))
| ~ product(X0,b,multiply(X0,b)) ),
inference(instantiation,[status(thm)],[c_186]) ).
tcf(c_336,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X1)
| ~ equalish(X0,X2)
| ~ product(identity,X0,X1) ),
inference(superposition,[status(thm)],[c_262,c_61]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(identity,X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_262,c_64]) ).
tcf(c_559,plain,
product(identity,c,c),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_560,plain,
product(inverse(c),c,identity),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_561,plain,
~ product(c,a,multiply(c,b)),
inference(superposition,[status(thm)],[c_227,c_66]) ).
tcf(c_682,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_336]) ).
tcf(c_684,plain,
equalish(b,a),
inference(superposition,[status(thm)],[c_65,c_682]) ).
tcf(c_699,plain,
( product(inverse(c),multiply(c,b),multiply(identity,b))
| ~ product(inverse(c),c,identity)
| ~ product(identity,b,multiply(identity,b))
| ~ product(c,b,multiply(c,b)) ),
inference(instantiation,[status(thm)],[c_314]) ).
tcf(c_757,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X1)
| ~ equalish(X0,X2)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_262,c_336]) ).
tcf(c_802,plain,
! [X0: $i] :
( product(inverse(inverse(X0)),identity,X0)
| ~ product(identity,X0,X0)
| ~ product(inverse(X0),X0,identity)
| ~ product(inverse(inverse(X0)),inverse(X0),identity) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_818,plain,
! [X0: $i] :
( product(identity,a,X0)
| ~ equalish(b,X0) ),
inference(superposition,[status(thm)],[c_65,c_351]) ).
tcf(c_829,plain,
! [X0: $i] :
( product(identity,b,X0)
| ~ equalish(a,X0) ),
inference(superposition,[status(thm)],[c_684,c_351]) ).
tcf(c_999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X2,X3,multiply(c,b))
| ~ product(identity,X3,X1)
| ~ product(X0,identity,X2)
| ~ product(X0,X1,multiply(c,b)) ),
inference(instantiation,[status(thm)],[c_152]) ).
tcf(c_1238,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ product(identity,X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_61]) ).
tcf(c_1248,plain,
! [X0: $i,X1: $i] :
( product(identity,a,X1)
| ~ equalish(b,X0)
| ~ equalish(X0,X1) ),
inference(superposition,[status(thm)],[c_818,c_64]) ).
tcf(c_1272,plain,
! [X0: $i] :
( equalish(b,X0)
| ~ equalish(a,X0) ),
inference(superposition,[status(thm)],[c_829,c_1238]) ).
tcf(c_1275,plain,
! [X0: $i] :
( equalish(a,X0)
| ~ equalish(b,X0) ),
inference(superposition,[status(thm)],[c_818,c_1238]) ).
tcf(c_1496,plain,
product(identity,b,multiply(identity,b)),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_1959,plain,
equalish(a,multiply(identity,b)),
inference(superposition,[status(thm)],[c_248,c_1275]) ).
tcf(c_2014,plain,
equalish(b,multiply(identity,b)),
inference(superposition,[status(thm)],[c_1959,c_1272]) ).
tcf(c_2338,plain,
! [X0: $i] :
( equalish(X0,multiply(identity,b))
| ~ equalish(b,X0) ),
inference(superposition,[status(thm)],[c_2014,c_757]) ).
tcf(c_4454,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X2,multiply(c,b))
| ~ product(identity,X2,X1)
| ~ product(inverse(inverse(X0)),identity,X0)
| ~ product(inverse(inverse(X0)),X1,multiply(c,b)) ),
inference(instantiation,[status(thm)],[c_999]) ).
tcf(c_4464,plain,
( product(inverse(inverse(c)),identity,c)
| ~ product(identity,c,c)
| ~ product(inverse(c),c,identity)
| ~ product(inverse(inverse(c)),inverse(c),identity) ),
inference(instantiation,[status(thm)],[c_802]) ).
tcf(c_5809,plain,
( product(inverse(inverse(c)),multiply(identity,b),multiply(c,b))
| ~ product(inverse(inverse(c)),inverse(c),identity)
| ~ product(identity,multiply(c,b),multiply(c,b))
| ~ product(inverse(c),multiply(c,b),multiply(identity,b)) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_9847,plain,
! [X0: $i] :
( product(identity,a,multiply(identity,b))
| ~ equalish(b,X0) ),
inference(superposition,[status(thm)],[c_2338,c_1248]) ).
tcf(c_9873,plain,
( product(identity,a,multiply(identity,b))
| ~ equalish(b,a) ),
inference(instantiation,[status(thm)],[c_9847]) ).
tcf(c_10587,plain,
product(inverse(inverse(c)),inverse(c),identity),
inference(instantiation,[status(thm)],[c_270]) ).
tcf(c_18433,plain,
! [X0: $i] :
( product(c,X0,multiply(c,b))
| ~ product(inverse(inverse(c)),identity,c)
| ~ product(identity,X0,multiply(identity,b))
| ~ product(inverse(inverse(c)),multiply(identity,b),multiply(c,b)) ),
inference(instantiation,[status(thm)],[c_4454]) ).
tcf(c_18434,plain,
( product(c,a,multiply(c,b))
| ~ product(identity,a,multiply(identity,b))
| ~ product(inverse(inverse(c)),identity,c)
| ~ product(inverse(inverse(c)),multiply(identity,b),multiply(c,b)) ),
inference(instantiation,[status(thm)],[c_18433]) ).
tcf(c_18435,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_18434,c_10587,c_9873,c_5809,c_4464,c_1496,c_699,c_684,c_561,c_560,c_559,c_165,c_164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP047-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 13:28:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 5.92/2.28 % SZS status Started for theBenchmark.p
% 5.92/2.28 % SZS status Unsatisfiable for theBenchmark.p
% 5.92/2.28
% 5.92/2.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.92/2.28
% 5.92/2.28 % ------ iProver source info
% 5.92/2.28
% 5.92/2.28 % git: date: 2026-07-19 20:42:38 +0200
% 5.92/2.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.92/2.28 % git: non_committed_changes: false
% 5.92/2.28
% 5.92/2.28 % ------ Parsing...% successful
% 5.92/2.28
% 5.92/2.28
% 5.92/2.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.92/2.28
% 5.92/2.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 5.92/2.28
% 5.92/2.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 5.92/2.28 % ------ Proving...
% 5.92/2.28 % ------ Problem Properties
% 5.92/2.28
% 5.92/2.28 %
% 5.92/2.28 % clauses 9
% 5.92/2.28 % conjectures 1
% 5.92/2.28 % EPR 6
% 5.92/2.28 % Horn 9
% 5.92/2.28 % unary 5
% 5.92/2.28 % binary 0
% 5.92/2.28 % lits 19
% 5.92/2.28 % lits eq 0
% 5.92/2.28 % fd_pure 0
% 5.92/2.28 % fd_pseudo 0
% 5.92/2.28 % fd_cond 0
% 5.92/2.28 % fd_pseudo_cond 0
% 5.92/2.28 % AC symbols 0
% 5.92/2.28
% 5.92/2.28 % ------ Input Options Time Limit: Unbounded
% 5.92/2.28
% 5.92/2.28
% 5.92/2.28 % ------
% 5.92/2.28 % Current options:
% 5.92/2.28 % ------
% 5.92/2.28
% 5.92/2.28
% 5.92/2.28 %
% 5.92/2.28
% 5.92/2.28 % ------ Proving...
% 5.92/2.28 %
% 5.92/2.28
% 5.92/2.28 % SZS status Unsatisfiable for theBenchmark.p
% 5.92/2.28
% 5.92/2.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.92/2.28
% 5.92/2.28
%------------------------------------------------------------------------------