%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 3.23s 1.19s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 78 ( 63 unt; 2 def)
% Number of atoms : 260 ( 69 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 77 ( 41 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 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 : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn 138 !; 0 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).
fof(f4,axiom,
! [X2,X0,X1] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
fof(f5,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
fof(f7,axiom,
! [X0] : product(multiplicative_identity,X0,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity4) ).
fof(f18,axiom,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
fof(f20,axiom,
! [X0] : product(X0,inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
fof(f29,axiom,
! [X0,X1] : sum(X0,multiply(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_and_multiply) ).
fof(f31,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associaticity_of_sum1) ).
fof(f33,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/theBenchmark.p',associaticity_of_product1) ).
fof(f35,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
fof(f36,plain,
x != inverse(inverse(x)),
inference(reorient_equations,[],[f35]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_88,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_90,plain,
! [X0: $i] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_95,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_101,plain,
! [X0: $i] : sum(X0,inverse(X0),multiplicative_identity),
inference(cnf_transformation,[],[f18]) ).
tcf(c_103,plain,
! [X0: $i] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[],[f20]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] : sum(X0,multiply(X0,X1),X0),
inference(cnf_transformation,[],[f29]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_116,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,[],[f33]) ).
tcf(c_118,negated_conjecture,
inverse(inverse(x)) != x,
inference(cnf_transformation,[],[f36]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = X0,
inference(well_definedness,[status(thm)],[c_112]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( add(X2,X5) = X4 )
| ( add(X1,X5) != X3 )
| ( add(X0,X3) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_114]) ).
tcf(c_146,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_116]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_86]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X1,X0) = X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_87]) ).
tcf(c_154,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_88]) ).
tcf(c_156,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_90]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X5,X1) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X0,X3) != X5 )
| ( multiply(X3,X1) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_95]) ).
tcf(c_175,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(well_definedness,[status(thm)],[c_101]) ).
tcf(c_177,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_103]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(unflattening,[status(thm)],[c_152]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_150]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_146]) ).
tcf(c_366,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_144]) ).
tcf(c_371,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(unflattening,[status(thm)],[c_164]) ).
tcf(c_433,definition,
iPr_def_10 = inverse(x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_434,definition,
iPr_def_11 = inverse(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_435,negated_conjecture,
iPr_def_11 != x,
inference(demodulation,[status(thm)],[c_118,c_433,c_434]) ).
tcf(c_514,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(superposition,[status(thm)],[c_366,c_359]) ).
tcf(c_517,plain,
add(iPr_def_10,iPr_def_11) = multiplicative_identity,
inference(superposition,[status(thm)],[c_434,c_175]) ).
tcf(c_520,plain,
! [X0: $i] : add(X0,inverse(X0)) = add(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_175,c_517]) ).
tcf(c_522,plain,
! [X0: $i] : multiply(add(iPr_def_10,iPr_def_11),X0) = X0,
inference(light_normalisation,[status(thm)],[c_156,c_517]) ).
tcf(c_523,plain,
! [X0: $i] : add(multiply(iPr_def_10,X0),multiply(iPr_def_11,X0)) = X0,
inference(demodulation,[status(thm)],[c_522,c_371]) ).
tcf(c_538,plain,
multiply(x,iPr_def_10) = additive_identity,
inference(superposition,[status(thm)],[c_433,c_177]) ).
tcf(c_540,plain,
multiply(iPr_def_10,iPr_def_11) = additive_identity,
inference(superposition,[status(thm)],[c_434,c_177]) ).
tcf(c_543,plain,
multiply(iPr_def_10,x) = additive_identity,
inference(theory_normalisation,[status(thm)],[c_538,c_365,c_357,c_366,c_359]) ).
tcf(c_548,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = multiply(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_177,c_540]) ).
tcf(c_551,plain,
! [X0: $i] : add(multiply(iPr_def_10,iPr_def_11),X0) = X0,
inference(demodulation,[status(thm)],[c_154,c_540]) ).
tcf(c_553,plain,
multiply(iPr_def_10,x) = multiply(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_543,c_540]) ).
tcf(c_554,plain,
add(multiply(iPr_def_10,iPr_def_11),multiply(iPr_def_11,x)) = x,
inference(superposition,[status(thm)],[c_553,c_523]) ).
tcf(c_562,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_357,c_142]) ).
tcf(c_586,plain,
! [X0: $i] : multiply(multiply(iPr_def_10,iPr_def_11),X0) = multiply(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_551,c_142]) ).
tcf(c_590,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(iPr_def_11,X0)) = multiply(iPr_def_10,iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_586,c_365,c_357,c_366,c_359]) ).
tcf(c_596,plain,
add(multiply(iPr_def_10,inverse(iPr_def_11)),multiply(iPr_def_10,iPr_def_11)) = inverse(iPr_def_11),
inference(superposition,[status(thm)],[c_548,c_523]) ).
tcf(c_598,plain,
add(multiply(iPr_def_10,iPr_def_11),multiply(iPr_def_10,inverse(iPr_def_11))) = inverse(iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_596,c_365,c_357,c_366,c_359]) ).
tcf(c_633,plain,
multiply(iPr_def_11,x) = x,
inference(demodulation,[status(thm)],[c_554,c_551]) ).
tcf(c_700,plain,
multiply(iPr_def_10,inverse(iPr_def_11)) = inverse(iPr_def_11),
inference(demodulation,[status(thm)],[c_598,c_551]) ).
tcf(c_701,plain,
add(iPr_def_10,inverse(iPr_def_11)) = iPr_def_10,
inference(superposition,[status(thm)],[c_700,c_142]) ).
tcf(c_741,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,add(multiply(X1,X0),X2)) = add(X0,X2),
inference(superposition,[status(thm)],[c_562,c_366]) ).
tcf(c_763,plain,
! [X0: $i] : add(iPr_def_10,add(inverse(iPr_def_11),X0)) = add(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_701,c_366]) ).
tcf(c_1038,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(inverse(X0),X1)) = multiply(add(iPr_def_10,iPr_def_11),X1),
inference(superposition,[status(thm)],[c_520,c_371]) ).
tcf(c_1952,plain,
! [X0: $i] : add(iPr_def_10,add(X0,inverse(iPr_def_11))) = add(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_701,c_514]) ).
tcf(c_2192,plain,
! [X0: $i] : add(iPr_def_10,add(inverse(iPr_def_11),X0)) = add(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_359,c_1952]) ).
tcf(c_2316,plain,
! [X0: $i,X1: $i] : multiply(add(iPr_def_10,add(inverse(iPr_def_11),X0)),X1) = add(multiply(X0,X1),multiply(iPr_def_10,X1)),
inference(superposition,[status(thm)],[c_2192,c_371]) ).
tcf(c_2333,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(iPr_def_10,X1)) = multiply(add(iPr_def_10,X0),X1),
inference(light_normalisation,[status(thm)],[c_2316,c_763]) ).
tcf(c_3178,plain,
! [X0: $i,X1: $i] : add(multiply(iPr_def_11,X0),add(multiply(iPr_def_10,iPr_def_11),X1)) = add(multiply(iPr_def_11,X0),X1),
inference(superposition,[status(thm)],[c_590,c_741]) ).
tcf(c_3254,plain,
! [X0: $i,X1: $i] : add(multiply(iPr_def_10,iPr_def_11),add(X0,multiply(iPr_def_11,X1))) = add(multiply(iPr_def_11,X1),X0),
inference(theory_normalisation,[status(thm)],[c_3178,c_365,c_357,c_366,c_359]) ).
tcf(c_8024,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_1038,c_523,c_551,c_2333,c_3254]) ).
tcf(c_8082,plain,
! [X0: $i] : add(multiply(x,X0),multiply(iPr_def_10,X0)) = X0,
inference(superposition,[status(thm)],[c_433,c_8024]) ).
tcf(c_8116,plain,
! [X0: $i] : add(multiply(iPr_def_10,X0),multiply(x,X0)) = X0,
inference(theory_normalisation,[status(thm)],[c_8082,c_365,c_357,c_366,c_359]) ).
tcf(c_8230,plain,
multiply(x,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_8116,c_551]) ).
tcf(c_8240,plain,
multiply(iPr_def_11,x) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_8230,c_365,c_357,c_366,c_359]) ).
tcf(c_8304,plain,
x = iPr_def_11,
inference(demodulation,[status(thm)],[c_633,c_8240]) ).
tcf(c_8355,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_435,c_8304]) ).
tcf(c_8356,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_8355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n003.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 06:32:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 3.23/1.19 % SZS status Started for theBenchmark.p
% 3.23/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.23/1.19
% 3.23/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.23/1.19
% 3.23/1.19 % ------ iProver source info
% 3.23/1.19
% 3.23/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.23/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.23/1.19 % git: non_committed_changes: false
% 3.23/1.19
% 3.23/1.19 % ------ Parsing...% successful
% 3.23/1.19
% 3.23/1.19
% 3.23/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.23/1.19
% 3.23/1.19 % ------ Preprocessing... sup_sim: 22 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 %
% 3.23/1.19
% 3.23/1.19 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.23/1.19 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.23/1.19
% 3.23/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.23/1.19 % ------ Proving...
% 3.23/1.19 % ------ Problem Properties
% 3.23/1.19
% 3.23/1.19 %
% 3.23/1.19 % clauses 23
% 3.23/1.19 % conjectures 1
% 3.23/1.19 % EPR 1
% 3.23/1.19 % Horn 23
% 3.23/1.19 % unary 23
% 3.23/1.19 % binary 0
% 3.23/1.19 % lits 23
% 3.23/1.19 % lits eq 23
% 3.23/1.19 % fd_pure 0
% 3.23/1.19 % fd_pseudo 0
% 3.23/1.19 % fd_cond 0
% 3.23/1.19 % fd_pseudo_cond 0
% 3.23/1.19 % AC symbols 2
% 3.23/1.19
% 3.23/1.19 % ------ Schedule UEQ
% 3.23/1.19
% 3.23/1.19 % ------ Option_UEQ Time Limit: 10.
% 3.23/1.19
% 3.23/1.19
% 3.23/1.19 % ------
% 3.23/1.19 % Current options:
% 3.23/1.19 % ------
% 3.23/1.19
% 3.23/1.19
% 3.23/1.19 %
% 3.23/1.19
% 3.23/1.19 % ------ Proving...
% 3.23/1.19 %
% 3.23/1.19
% 3.23/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.23/1.19
% 3.23/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.23/1.19
%------------------------------------------------------------------------------