%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO006-1 : 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 : n016.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 01:00:09 PM UTC 2026
% Result : Unsatisfiable 3.59s 1.19s
% Output : CNFRefutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 60 ( 45 unt; 1 def)
% Number of atoms : 195 ( 49 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 90 ( 48 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 133 ( 0 sgn 133 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/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/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(f6,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
fof(f7,axiom,
! [X0] : product(multiplicative_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
fof(f8,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
fof(f10,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity2) ).
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(f14,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X0,X5,X6)
| ~ product(X2,X4,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity6) ).
fof(f18,axiom,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
fof(f20,axiom,
! [X0] : product(X0,inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
fof(f23,negated_conjecture,
~ product(x,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equations) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_76,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_77,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_78,plain,
! [X0: $i] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_79,plain,
! [X0: $i] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[],[f8]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sum(X6,X2,X5)
| ~ sum(X6,X1,X4)
| ~ sum(X6,X0,X3)
| ~ product(X3,X4,X5)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_89,plain,
! [X0: $i] : sum(X0,inverse(X0),multiplicative_identity),
inference(cnf_transformation,[],[f18]) ).
tcf(c_91,plain,
! [X0: $i] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
~ product(x,additive_identity,additive_identity),
inference(cnf_transformation,[],[f23]) ).
tcf(c_106,plain,
multiply(x,additive_identity) != additive_identity,
inference(well_definedness,[status(thm)],[c_94]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_74]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X1,X0) = X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_75]) ).
tcf(c_113,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_76]) ).
tcf(c_114,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(well_definedness,[status(thm)],[c_77]) ).
tcf(c_115,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_78]) ).
tcf(c_116,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X6,X2) = X5 )
| ( multiply(X6,X1) != X4 )
| ( multiply(X6,X0) != X3 )
| ( add(X3,X4) != X5 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_81]) ).
tcf(c_123,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_83]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( add(X0,X5) = X6 )
| ( multiply(X2,X4) != X6 )
| ( multiply(X1,X3) != X5 )
| ( add(X0,X3) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_85]) ).
tcf(c_134,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(well_definedness,[status(thm)],[c_89]) ).
tcf(c_136,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_91]) ).
tcf(c_274,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(unflattening,[status(thm)],[c_111]) ).
tcf(c_275,plain,
multiply(additive_identity,x) != additive_identity,
inference(demodulation,[status(thm)],[c_106,c_274]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_109]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_127]) ).
tcf(c_285,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(unflattening,[status(thm)],[c_123]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_119]) ).
tcf(c_327,definition,
iPr_def_10 = multiply(additive_identity,x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_328,plain,
iPr_def_10 != additive_identity,
inference(demodulation,[status(thm)],[c_275,c_327]) ).
tcf(c_437,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(multiply(X0,X0),multiply(X0,X1)),add(multiply(X2,X0),multiply(X2,X1))) = add(X0,multiply(X2,X1)),
inference(demodulation,[status(thm)],[c_283,c_285,c_287]) ).
tcf(c_693,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = multiply(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_134,c_287]) ).
tcf(c_727,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = X0,
inference(light_normalisation,[status(thm)],[c_693,c_116]) ).
tcf(c_831,plain,
! [X0: $i] : add(X0,multiply(multiplicative_identity,inverse(X0))) = multiplicative_identity,
inference(superposition,[status(thm)],[c_115,c_727]) ).
tcf(c_843,plain,
! [X0: $i] : add(multiply(X0,X0),additive_identity) = X0,
inference(superposition,[status(thm)],[c_136,c_727]) ).
tcf(c_853,plain,
! [X0: $i,X1: $i] : add(add(multiply(X0,X0),multiply(X0,inverse(X0))),X1) = add(X0,multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_727,c_437]) ).
tcf(c_861,plain,
! [X0: $i,X1: $i] : add(add(multiply(X0,X0),additive_identity),X1) = add(X0,multiply(X1,inverse(X0))),
inference(light_normalisation,[status(thm)],[c_853,c_136]) ).
tcf(c_876,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_843,c_114]) ).
tcf(c_923,plain,
! [X0: $i] : add(multiplicative_identity,X0) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_831,c_114,c_277,c_861,c_876]) ).
tcf(c_929,plain,
! [X0: $i,X1: $i] : add(multiply(multiplicative_identity,X0),multiply(X1,X0)) = multiply(multiplicative_identity,X0),
inference(superposition,[status(thm)],[c_923,c_285]) ).
tcf(c_930,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_929,c_115]) ).
tcf(c_957,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_930,c_113]) ).
tcf(c_970,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(superposition,[status(thm)],[c_957,c_274]) ).
tcf(c_975,plain,
additive_identity = iPr_def_10,
inference(demodulation,[status(thm)],[c_327,c_970]) ).
tcf(c_983,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_328,c_975]) ).
tcf(c_984,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_983]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 06:30:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.59/1.19 % SZS status Started for theBenchmark.p
% 3.59/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.59/1.19
% 3.59/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.59/1.19
% 3.59/1.19 % ------ iProver source info
% 3.59/1.19
% 3.59/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.59/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.59/1.19 % git: non_committed_changes: false
% 3.59/1.19
% 3.59/1.19 % ------ Parsing...% successful
% 3.59/1.19
% 3.59/1.19
% 3.59/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.59/1.19
% 3.59/1.19 % ------ Preprocessing... sup_sim: 19 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 %
% 3.59/1.19
% 3.59/1.19 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.59/1.19 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.59/1.19
% 3.59/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.59/1.19 % ------ Proving...
% 3.59/1.19 % ------ Problem Properties
% 3.59/1.19
% 3.59/1.19 %
% 3.59/1.19 % clauses 14
% 3.59/1.19 % conjectures 0
% 3.59/1.19 % EPR 1
% 3.59/1.19 % Horn 14
% 3.59/1.19 % unary 14
% 3.59/1.19 % binary 0
% 3.59/1.19 % lits 14
% 3.59/1.19 % lits eq 14
% 3.59/1.19 % fd_pure 0
% 3.59/1.19 % fd_pseudo 0
% 3.59/1.19 % fd_cond 0
% 3.59/1.19 % fd_pseudo_cond 0
% 3.59/1.19 % AC symbols 0
% 3.59/1.19
% 3.59/1.19 % ------ Schedule UEQ
% 3.59/1.19
% 3.59/1.19 % ------ Option_UEQ Time Limit: 10.
% 3.59/1.19
% 3.59/1.19
% 3.59/1.19 % ------
% 3.59/1.19 % Current options:
% 3.59/1.19 % ------
% 3.59/1.19
% 3.59/1.19
% 3.59/1.19 %
% 3.59/1.19
% 3.59/1.19 % ------ Proving...
% 3.59/1.19 %
% 3.59/1.19
% 3.59/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.59/1.19
% 3.59/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.59/1.19
%------------------------------------------------------------------------------