%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP012-3 : 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 : n009.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 3.19s 1.33s
% Output : CNFRefutation 3.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 38 ( 35 unt; 5 def)
% Number of atoms : 79 ( 30 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 21 ( 12 ~; 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 : 8 ( 6 usr; 6 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?; 28 :)
% 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,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_product_is_product_of_inverses) ).
tcf(c_58,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_59,plain,
! [X0: $i] : product(X0,identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_60,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f3]) ).
tcf(c_61,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f4]) ).
tcf(c_65,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_66,negated_conjecture,
multiply(inverse(b),inverse(a)) != inverse(multiply(a,b)),
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_58]) ).
tcf(c_73,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(well_definedness,[status(thm)],[c_59]) ).
tcf(c_74,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(well_definedness,[status(thm)],[c_60]) ).
tcf(c_75,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(well_definedness,[status(thm)],[c_61]) ).
tcf(c_81,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_65]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_81]) ).
tcf(c_146,definition,
iPr_def_10 = inverse(b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_147,definition,
iPr_def_11 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_148,definition,
iPr_def_12 = multiply(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_149,definition,
iPr_def_13 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_150,definition,
iPr_def_14 = inverse(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_151,negated_conjecture,
iPr_def_12 != iPr_def_14,
inference(demodulation,[status(thm)],[c_66,c_149,c_150,c_147,c_146,c_148]) ).
tcf(c_201,plain,
multiply(iPr_def_14,iPr_def_13) = identity,
inference(superposition,[status(thm)],[c_150,c_74]) ).
tcf(c_204,plain,
multiply(b,iPr_def_10) = identity,
inference(superposition,[status(thm)],[c_146,c_75]) ).
tcf(c_205,plain,
multiply(a,iPr_def_11) = identity,
inference(superposition,[status(thm)],[c_147,c_75]) ).
tcf(c_212,plain,
! [X0: $i] : multiply(a,multiply(b,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_149,c_123]) ).
tcf(c_221,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_13,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_201,c_123]) ).
tcf(c_222,plain,
! [X0: $i] : multiply(b,multiply(iPr_def_10,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_204,c_123]) ).
tcf(c_230,plain,
! [X0: $i] : multiply(b,multiply(iPr_def_10,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_222,c_72]) ).
tcf(c_231,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_13,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_221,c_72]) ).
tcf(c_253,plain,
multiply(b,iPr_def_12) = iPr_def_11,
inference(superposition,[status(thm)],[c_148,c_230]) ).
tcf(c_265,plain,
multiply(a,iPr_def_11) = multiply(iPr_def_13,iPr_def_12),
inference(superposition,[status(thm)],[c_253,c_212]) ).
tcf(c_267,plain,
multiply(iPr_def_13,iPr_def_12) = identity,
inference(light_normalisation,[status(thm)],[c_265,c_205]) ).
tcf(c_284,plain,
multiply(iPr_def_14,identity) = iPr_def_12,
inference(superposition,[status(thm)],[c_267,c_231]) ).
tcf(c_296,plain,
iPr_def_12 = iPr_def_14,
inference(demodulation,[status(thm)],[c_284,c_73]) ).
tcf(c_297,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_296,c_151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 13:13:28 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 3.19/1.33 % SZS status Started for theBenchmark.p
% 3.19/1.33 % SZS status Unsatisfiable for theBenchmark.p
% 3.19/1.33
% 3.19/1.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.19/1.33
% 3.19/1.33 % ------ iProver source info
% 3.19/1.33
% 3.19/1.33 % git: date: 2026-07-19 20:42:38 +0200
% 3.19/1.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.19/1.33 % git: non_committed_changes: false
% 3.19/1.33
% 3.19/1.33 % ------ Parsing...% successful
% 3.19/1.33
% 3.19/1.33
% 3.19/1.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.19/1.33
% 3.19/1.33 % ------ 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 %
% 3.19/1.33
% 3.19/1.33 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.19/1.33 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.19/1.33
% 3.19/1.33 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.19/1.33 % ------ Proving...
% 3.19/1.33 % ------ Problem Properties
% 3.19/1.33
% 3.19/1.33 %
% 3.19/1.33 % clauses 11
% 3.19/1.33 % conjectures 1
% 3.19/1.33 % EPR 1
% 3.19/1.33 % Horn 11
% 3.19/1.33 % unary 11
% 3.19/1.33 % binary 0
% 3.19/1.33 % lits 11
% 3.19/1.33 % lits eq 11
% 3.19/1.33 % fd_pure 0
% 3.19/1.33 % fd_pseudo 0
% 3.19/1.33 % fd_cond 0
% 3.19/1.33 % fd_pseudo_cond 0
% 3.19/1.33 % AC symbols 0
% 3.19/1.33
% 3.19/1.33 % ------ Schedule UEQ
% 3.19/1.33
% 3.19/1.33 % ------ Option_UEQ Time Limit: 10.
% 3.19/1.33
% 3.19/1.33
% 3.19/1.33 % ------
% 3.19/1.33 % Current options:
% 3.19/1.33 % ------
% 3.19/1.33
% 3.19/1.33
% 3.19/1.33 %
% 3.19/1.33
% 3.19/1.33 % ------ Proving...
% 3.19/1.33 %
% 3.19/1.33
% 3.19/1.33 % SZS status Unsatisfiable for theBenchmark.p
% 3.19/1.33
% 3.19/1.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.19/1.33
% 3.19/1.33
%------------------------------------------------------------------------------