%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO013-3 : 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 01:00:13 PM UTC 2026
% Result : Unsatisfiable 3.53s 1.27s
% Output : CNFRefutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 46 unt; 4 def)
% Number of atoms : 134 ( 40 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X2,X0,X1] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
fof(f5,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
fof(f7,axiom,
! [X0] : product(multiplicative_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
fof(f12,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity4) ).
fof(f24,negated_conjecture,
sum(x,y,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_to_multiplicative_identity1) ).
fof(f25,negated_conjecture,
sum(x,z,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_to_multiplicative_identity2) ).
fof(f26,negated_conjecture,
product(x,y,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_additive_identity1) ).
fof(f27,negated_conjecture,
product(x,z,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_additive_identity2) ).
fof(f28,negated_conjecture,
y != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_inverse_are_equal) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_81,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_83,plain,
! [X0: $i] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X2,X6,X5)
| ~ product(X1,X6,X4)
| ~ product(X0,X6,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_100,negated_conjecture,
sum(x,y,multiplicative_identity),
inference(cnf_transformation,[],[f24]) ).
tcf(c_101,negated_conjecture,
sum(x,z,multiplicative_identity),
inference(cnf_transformation,[],[f25]) ).
tcf(c_102,negated_conjecture,
product(x,y,additive_identity),
inference(cnf_transformation,[],[f26]) ).
tcf(c_103,negated_conjecture,
product(x,z,additive_identity),
inference(cnf_transformation,[],[f27]) ).
tcf(c_104,negated_conjecture,
y != z,
inference(cnf_transformation,[],[f28]) ).
tcf(c_117,plain,
add(x,y) = multiplicative_identity,
inference(well_definedness,[status(thm)],[c_100]) ).
tcf(c_118,plain,
add(x,z) = multiplicative_identity,
inference(well_definedness,[status(thm)],[c_101]) ).
tcf(c_119,plain,
multiply(x,y) = additive_identity,
inference(well_definedness,[status(thm)],[c_102]) ).
tcf(c_120,plain,
multiply(x,z) = additive_identity,
inference(well_definedness,[status(thm)],[c_103]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X1,X0) = X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_80]) ).
tcf(c_127,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_81]) ).
tcf(c_129,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_83]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X2,X6) = X5 )
| ( multiply(X1,X6) != X4 )
| ( multiply(X0,X6) != X3 )
| ( add(X3,X4) != X5 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_88]) ).
tcf(c_298,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(unflattening,[status(thm)],[c_125]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(unflattening,[status(thm)],[c_137]) ).
tcf(c_362,definition,
iPr_def_10 = multiply(x,z),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_363,definition,
iPr_def_11 = multiply(x,y),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_364,definition,
iPr_def_12 = add(x,z),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_365,definition,
iPr_def_13 = add(x,y),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_366,plain,
iPr_def_10 = additive_identity,
inference(demodulation,[status(thm)],[c_120,c_362]) ).
tcf(c_367,plain,
iPr_def_11 = additive_identity,
inference(demodulation,[status(thm)],[c_119,c_363]) ).
tcf(c_368,plain,
iPr_def_12 = multiplicative_identity,
inference(demodulation,[status(thm)],[c_118,c_364]) ).
tcf(c_369,plain,
iPr_def_13 = multiplicative_identity,
inference(demodulation,[status(thm)],[c_117,c_365]) ).
tcf(c_370,negated_conjecture,
y != z,
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_446,plain,
iPr_def_10 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_367,c_366]) ).
tcf(c_447,plain,
iPr_def_12 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_369,c_368]) ).
tcf(c_448,plain,
! [X0: $i] : add(iPr_def_10,X0) = X0,
inference(light_normalisation,[status(thm)],[c_127,c_366]) ).
tcf(c_450,plain,
! [X0: $i] : multiply(iPr_def_12,X0) = X0,
inference(light_normalisation,[status(thm)],[c_129,c_368]) ).
tcf(c_451,plain,
multiply(x,y) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_363,c_446]) ).
tcf(c_452,plain,
add(x,y) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_365,c_447]) ).
tcf(c_619,plain,
! [X0: $i] : add(multiply(x,X0),multiply(y,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_452,c_308]) ).
tcf(c_620,plain,
! [X0: $i] : add(multiply(x,X0),multiply(z,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_364,c_308]) ).
tcf(c_647,plain,
! [X0: $i] : add(multiply(x,X0),multiply(z,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_620,c_450]) ).
tcf(c_648,plain,
! [X0: $i] : add(multiply(x,X0),multiply(y,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_619,c_450]) ).
tcf(c_655,plain,
add(iPr_def_10,multiply(z,y)) = y,
inference(superposition,[status(thm)],[c_451,c_647]) ).
tcf(c_668,plain,
add(iPr_def_10,multiply(y,z)) = z,
inference(superposition,[status(thm)],[c_362,c_648]) ).
tcf(c_725,plain,
multiply(y,z) = z,
inference(demodulation,[status(thm)],[c_668,c_448]) ).
tcf(c_787,plain,
y = z,
inference(demodulation,[status(thm)],[c_655,c_298,c_448,c_725]) ).
tcf(c_788,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_787,c_370]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO013-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 06:31:34 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 3.53/1.27 % SZS status Started for theBenchmark.p
% 3.53/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.53/1.27
% 3.53/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.53/1.27
% 3.53/1.27 % ------ iProver source info
% 3.53/1.27
% 3.53/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.53/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.53/1.27 % git: non_committed_changes: false
% 3.53/1.27
% 3.53/1.27 % ------ Parsing...% successful
% 3.53/1.27
% 3.53/1.27
% 3.53/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.53/1.27
% 3.53/1.27 % ------ Preprocessing... sup_sim: 18 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 %
% 3.53/1.27
% 3.53/1.27 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.53/1.27 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.53/1.27
% 3.53/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.53/1.27 % ------ Proving...
% 3.53/1.27 % ------ Problem Properties
% 3.53/1.27
% 3.53/1.27 %
% 3.53/1.27 % clauses 22
% 3.53/1.27 % conjectures 1
% 3.53/1.27 % EPR 5
% 3.53/1.27 % Horn 22
% 3.53/1.27 % unary 22
% 3.53/1.27 % binary 0
% 3.53/1.27 % lits 22
% 3.53/1.27 % lits eq 22
% 3.53/1.27 % fd_pure 0
% 3.53/1.27 % fd_pseudo 0
% 3.53/1.27 % fd_cond 0
% 3.53/1.27 % fd_pseudo_cond 0
% 3.53/1.27 % AC symbols 0
% 3.53/1.27
% 3.53/1.27 % ------ Schedule UEQ
% 3.53/1.27
% 3.53/1.27 % ------ Option_UEQ Time Limit: 10.
% 3.53/1.27
% 3.53/1.27
% 3.53/1.27 % ------
% 3.53/1.27 % Current options:
% 3.53/1.27 % ------
% 3.53/1.27
% 3.53/1.27
% 3.53/1.27 %
% 3.53/1.27
% 3.53/1.27 % ------ Proving...
% 3.53/1.27 %
% 3.53/1.27
% 3.53/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.53/1.27
% 3.53/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.53/1.27
% 3.53/1.27
%------------------------------------------------------------------------------