%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO013-1 : 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 : n017.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 01:00:12 PM UTC 2026
% Result : Unsatisfiable 1.19s 1.09s
% Output : CNFRefutation 1.19s
% 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(f23,negated_conjecture,
sum(x,y,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_to_multiplicative_identity1) ).
fof(f24,negated_conjecture,
sum(x,z,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_to_multiplicative_identity2) ).
fof(f25,negated_conjecture,
product(x,y,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_additive_identity1) ).
fof(f26,negated_conjecture,
product(x,z,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_additive_identity2) ).
fof(f27,negated_conjecture,
y != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_inverse_are_equal) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_80,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_82,plain,
! [X0: $i] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_87,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_98,negated_conjecture,
sum(x,y,multiplicative_identity),
inference(cnf_transformation,[],[f23]) ).
tcf(c_99,negated_conjecture,
sum(x,z,multiplicative_identity),
inference(cnf_transformation,[],[f24]) ).
tcf(c_100,negated_conjecture,
product(x,y,additive_identity),
inference(cnf_transformation,[],[f25]) ).
tcf(c_101,negated_conjecture,
product(x,z,additive_identity),
inference(cnf_transformation,[],[f26]) ).
tcf(c_102,negated_conjecture,
y != z,
inference(cnf_transformation,[],[f27]) ).
tcf(c_114,plain,
add(x,y) = multiplicative_identity,
inference(well_definedness,[status(thm)],[c_98]) ).
tcf(c_115,plain,
add(x,z) = multiplicative_identity,
inference(well_definedness,[status(thm)],[c_99]) ).
tcf(c_116,plain,
multiply(x,y) = additive_identity,
inference(well_definedness,[status(thm)],[c_100]) ).
tcf(c_117,plain,
multiply(x,z) = additive_identity,
inference(well_definedness,[status(thm)],[c_101]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X1,X0) = X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_124,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_80]) ).
tcf(c_126,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_82]) ).
tcf(c_134,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_87]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(unflattening,[status(thm)],[c_122]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(unflattening,[status(thm)],[c_134]) ).
tcf(c_353,definition,
iPr_def_10 = multiply(x,z),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_354,definition,
iPr_def_11 = multiply(x,y),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_355,definition,
iPr_def_12 = add(x,z),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_356,definition,
iPr_def_13 = add(x,y),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_357,plain,
iPr_def_10 = additive_identity,
inference(demodulation,[status(thm)],[c_117,c_353]) ).
tcf(c_358,plain,
iPr_def_11 = additive_identity,
inference(demodulation,[status(thm)],[c_116,c_354]) ).
tcf(c_359,plain,
iPr_def_12 = multiplicative_identity,
inference(demodulation,[status(thm)],[c_115,c_355]) ).
tcf(c_360,plain,
iPr_def_13 = multiplicative_identity,
inference(demodulation,[status(thm)],[c_114,c_356]) ).
tcf(c_361,negated_conjecture,
y != z,
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_429,plain,
iPr_def_10 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_358,c_357]) ).
tcf(c_430,plain,
iPr_def_12 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_360,c_359]) ).
tcf(c_431,plain,
! [X0: $i] : add(iPr_def_10,X0) = X0,
inference(light_normalisation,[status(thm)],[c_124,c_357]) ).
tcf(c_433,plain,
! [X0: $i] : multiply(iPr_def_12,X0) = X0,
inference(light_normalisation,[status(thm)],[c_126,c_359]) ).
tcf(c_435,plain,
multiply(x,y) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_354,c_429]) ).
tcf(c_436,plain,
add(x,y) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_356,c_430]) ).
tcf(c_694,plain,
! [X0: $i] : add(multiply(x,X0),multiply(y,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_436,c_303]) ).
tcf(c_695,plain,
! [X0: $i] : add(multiply(x,X0),multiply(z,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_355,c_303]) ).
tcf(c_738,plain,
! [X0: $i] : add(multiply(x,X0),multiply(z,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_695,c_433]) ).
tcf(c_739,plain,
! [X0: $i] : add(multiply(x,X0),multiply(y,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_694,c_433]) ).
tcf(c_751,plain,
add(iPr_def_10,multiply(z,y)) = y,
inference(superposition,[status(thm)],[c_435,c_738]) ).
tcf(c_1004,plain,
add(iPr_def_10,multiply(y,z)) = z,
inference(superposition,[status(thm)],[c_353,c_739]) ).
tcf(c_1020,plain,
multiply(y,z) = z,
inference(demodulation,[status(thm)],[c_1004,c_431]) ).
tcf(c_1027,plain,
y = z,
inference(demodulation,[status(thm)],[c_751,c_293,c_431,c_1020]) ).
tcf(c_1028,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1027,c_361]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 06:26:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 1.19/1.09 % SZS status Started for theBenchmark.p
% 1.19/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 1.19/1.09
% 1.19/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.19/1.09
% 1.19/1.09 % ------ iProver source info
% 1.19/1.09
% 1.19/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 1.19/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.19/1.09 % git: non_committed_changes: false
% 1.19/1.09
% 1.19/1.09 % ------ Parsing...% successful
% 1.19/1.09
% 1.19/1.09
% 1.19/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.19/1.09
% 1.19/1.09 % ------ 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 %
% 1.19/1.09
% 1.19/1.09 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 1.19/1.09 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.19/1.09
% 1.19/1.09 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.19/1.09 % ------ Proving...
% 1.19/1.09 % ------ Problem Properties
% 1.19/1.09
% 1.19/1.09 %
% 1.19/1.09 % clauses 21
% 1.19/1.09 % conjectures 1
% 1.19/1.09 % EPR 5
% 1.19/1.09 % Horn 21
% 1.19/1.09 % unary 21
% 1.19/1.09 % binary 0
% 1.19/1.09 % lits 21
% 1.19/1.09 % lits eq 21
% 1.19/1.09 % fd_pure 0
% 1.19/1.09 % fd_pseudo 0
% 1.19/1.09 % fd_cond 0
% 1.19/1.09 % fd_pseudo_cond 0
% 1.19/1.09 % AC symbols 0
% 1.19/1.09
% 1.19/1.09 % ------ Schedule UEQ
% 1.19/1.09
% 1.19/1.09 % ------ Option_UEQ Time Limit: 10.
% 1.19/1.09
% 1.19/1.09
% 1.19/1.09 % ------
% 1.19/1.09 % Current options:
% 1.19/1.09 % ------
% 1.19/1.09
% 1.19/1.09
% 1.19/1.09 %
% 1.19/1.09
% 1.19/1.09 % ------ Proving...
% 1.19/1.09 %
% 1.19/1.09
% 1.19/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 1.19/1.09
% 1.19/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.19/1.09
% 1.19/1.09
%------------------------------------------------------------------------------