%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP031-1 : 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 : n019.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 01:29:58 PM UTC 2026
% Result : Unsatisfiable 3.12s 1.28s
% Output : CNFRefutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 16 unt; 0 def)
% Number of atoms : 48 ( 13 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,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/GRP002-0.ax',associativity2) ).
fof(f5,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f6,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f7,negated_conjecture,
! [X0] : ~ product(a,X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_has_an_inverse) ).
tcf(c_59,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,[],[f4]) ).
tcf(c_60,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_61,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f6]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] : ~ product(a,X0,identity),
inference(cnf_transformation,[],[f7]) ).
tcf(c_68,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_60]) ).
tcf(c_69,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(well_definedness,[status(thm)],[c_61]) ).
tcf(c_70,plain,
! [X0: $i] : multiply(a,X0) != identity,
inference(well_definedness,[status(thm)],[c_62]) ).
tcf(c_76,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_59]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_76]) ).
tcf(c_131,plain,
! [X0: $i] : multiply(a,X0) != identity,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_69,c_114]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_159,c_68]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_163,c_163]) ).
tcf(c_229,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_167,c_69]) ).
tcf(c_249,plain,
$false,
inference(superposition,[status(thm)],[c_229,c_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP031-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 13:19:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.12/1.28 % SZS status Started for theBenchmark.p
% 3.12/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 3.12/1.28
% 3.12/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.12/1.28
% 3.12/1.28 % ------ iProver source info
% 3.12/1.28
% 3.12/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.12/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.12/1.28 % git: non_committed_changes: false
% 3.12/1.28
% 3.12/1.28 % ------ Parsing...% successful
% 3.12/1.28
% 3.12/1.28
% 3.12/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.12/1.28
% 3.12/1.28 % ------ Preprocessing... sup_sim: 4 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.12/1.28
% 3.12/1.28 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.12/1.28 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.12/1.28
% 3.12/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.12/1.28 % ------ Proving...
% 3.12/1.28 % ------ Problem Properties
% 3.12/1.28
% 3.12/1.28 %
% 3.12/1.28 % clauses 4
% 3.12/1.28 % conjectures 0
% 3.12/1.28 % EPR 0
% 3.12/1.28 % Horn 4
% 3.12/1.28 % unary 4
% 3.12/1.28 % binary 0
% 3.12/1.28 % lits 4
% 3.12/1.28 % lits eq 4
% 3.12/1.28 % fd_pure 0
% 3.12/1.28 % fd_pseudo 0
% 3.12/1.28 % fd_cond 0
% 3.12/1.28 % fd_pseudo_cond 0
% 3.12/1.28 % AC symbols 0
% 3.12/1.28
% 3.12/1.28 % ------ Schedule UEQ
% 3.12/1.28
% 3.12/1.28 % ------ Option_UEQ Time Limit: 10.
% 3.12/1.28
% 3.12/1.28
% 3.12/1.28 % ------
% 3.12/1.28 % Current options:
% 3.12/1.28 % ------
% 3.12/1.28
% 3.12/1.28
% 3.12/1.28 %
% 3.12/1.28
% 3.12/1.28 % ------ Proving...
% 3.12/1.28 %
% 3.12/1.28
% 3.12/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 3.12/1.28
% 3.12/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.12/1.28
% 3.12/1.28
%------------------------------------------------------------------------------