%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP012-2 : 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 : n006.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 01:29:54 PM UTC 2026
% Result : Unsatisfiable 3.22s 1.16s
% Output : CNFRefutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 39 unt; 1 def)
% Number of atoms : 96 ( 30 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 23 ( 14 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 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 : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
fof(f9,axiom,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_multiply_b_is_c) ).
fof(f10,axiom,
product(inverse(b),inverse(a),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_b_multiply_inverse_a_is_d) ).
fof(f11,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_inverse_equals_d) ).
fof(f12,plain,
d != inverse(c),
inference(reorient_equations,[],[f11]) ).
tcf(c_60,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_61,plain,
! [X0: $i] : product(X0,identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_62,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f3]) ).
tcf(c_63,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,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_68,plain,
product(a,b,c),
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,plain,
product(inverse(b),inverse(a),d),
inference(cnf_transformation,[],[f10]) ).
tcf(c_70,negated_conjecture,
inverse(c) != d,
inference(cnf_transformation,[],[f12]) ).
tcf(c_76,plain,
multiply(a,b) = c,
inference(well_definedness,[status(thm)],[c_68]) ).
tcf(c_77,plain,
multiply(inverse(b),inverse(a)) = d,
inference(well_definedness,[status(thm)],[c_69]) ).
tcf(c_78,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_60]) ).
tcf(c_79,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(well_definedness,[status(thm)],[c_61]) ).
tcf(c_80,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(well_definedness,[status(thm)],[c_62]) ).
tcf(c_81,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(well_definedness,[status(thm)],[c_63]) ).
tcf(c_87,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_67]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_87]) ).
tcf(c_160,definition,
iPr_def_10 = inverse(c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_161,negated_conjecture,
iPr_def_10 != d,
inference(demodulation,[status(thm)],[c_70,c_160]) ).
tcf(c_205,plain,
multiply(iPr_def_10,c) = identity,
inference(superposition,[status(thm)],[c_160,c_80]) ).
tcf(c_214,plain,
! [X0: $i] : multiply(a,multiply(b,X0)) = multiply(c,X0),
inference(superposition,[status(thm)],[c_76,c_133]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_80,c_133]) ).
tcf(c_221,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(c,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_205,c_133]) ).
tcf(c_227,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(c,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_221,c_78]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_218,c_78]) ).
tcf(c_259,plain,
multiply(inverse(inverse(b)),d) = inverse(a),
inference(superposition,[status(thm)],[c_77,c_254]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_254,c_254]) ).
tcf(c_286,plain,
multiply(b,d) = inverse(a),
inference(demodulation,[status(thm)],[c_259,c_273]) ).
tcf(c_289,plain,
multiply(a,inverse(a)) = multiply(c,d),
inference(superposition,[status(thm)],[c_286,c_214]) ).
tcf(c_407,plain,
multiply(c,d) = identity,
inference(demodulation,[status(thm)],[c_289,c_81]) ).
tcf(c_410,plain,
multiply(iPr_def_10,identity) = d,
inference(superposition,[status(thm)],[c_407,c_227]) ).
tcf(c_413,plain,
d = iPr_def_10,
inference(demodulation,[status(thm)],[c_410,c_79]) ).
tcf(c_420,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_161,c_413]) ).
tcf(c_421,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_420]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-2 : 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 : n006.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 13:12:56 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.22/1.16 % SZS status Started for theBenchmark.p
% 3.22/1.16 % SZS status Unsatisfiable for theBenchmark.p
% 3.22/1.16
% 3.22/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.22/1.16
% 3.22/1.16 % ------ iProver source info
% 3.22/1.16
% 3.22/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 3.22/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.22/1.16 % git: non_committed_changes: false
% 3.22/1.16
% 3.22/1.16 % ------ Parsing...% successful
% 3.22/1.16
% 3.22/1.16
% 3.22/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.22/1.16
% 3.22/1.16 % ------ 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 %
% 3.22/1.16
% 3.22/1.16 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.22/1.16 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.22/1.16
% 3.22/1.16 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.22/1.16 % ------ Proving...
% 3.22/1.16 % ------ Problem Properties
% 3.22/1.16
% 3.22/1.16 %
% 3.22/1.16 % clauses 9
% 3.22/1.16 % conjectures 1
% 3.22/1.16 % EPR 1
% 3.22/1.16 % Horn 9
% 3.22/1.16 % unary 9
% 3.22/1.16 % binary 0
% 3.22/1.16 % lits 9
% 3.22/1.16 % lits eq 9
% 3.22/1.16 % fd_pure 0
% 3.22/1.16 % fd_pseudo 0
% 3.22/1.16 % fd_cond 0
% 3.22/1.16 % fd_pseudo_cond 0
% 3.22/1.16 % AC symbols 0
% 3.22/1.16
% 3.22/1.16 % ------ Schedule UEQ
% 3.22/1.16
% 3.22/1.16 % ------ Option_UEQ Time Limit: 10.
% 3.22/1.16
% 3.22/1.16
% 3.22/1.16 % ------
% 3.22/1.16 % Current options:
% 3.22/1.16 % ------
% 3.22/1.16
% 3.22/1.16
% 3.22/1.16 %
% 3.22/1.16
% 3.22/1.16 % ------ Proving...
% 3.22/1.16 %
% 3.22/1.16
% 3.22/1.16 % SZS status Unsatisfiable for theBenchmark.p
% 3.22/1.16
% 3.22/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.22/1.16
% 3.22/1.16
%------------------------------------------------------------------------------