%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO003-1 : 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 : n002.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 01:00:08 PM UTC 2026
% Result : Unsatisfiable 0.71s 1.28s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 38 unt; 1 def)
% Number of atoms : 205 ( 47 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 107 ( 56 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 139 ( 0 sgn 139 !; 0 ?; 103 :)
% 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(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(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(f16,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X5,X1,X6)
| ~ product(X2,X4,X6)
| ~ product(X0,X3,X5)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity8) ).
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,x,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_equalities) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
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_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_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sum(X2,X6,X5)
| ~ sum(X1,X6,X4)
| ~ sum(X0,X6,X3)
| ~ product(X3,X4,X5)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
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,x,x),
inference(cnf_transformation,[],[f23]) ).
tcf(c_106,plain,
multiply(x,x) != x,
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_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_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_131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( add(X5,X1) = X6 )
| ( multiply(X2,X4) != X6 )
| ( multiply(X0,X3) != X5 )
| ( add(X3,X1) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_87]) ).
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_276,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_109]) ).
tcf(c_280,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X2,X1)) = add(multiply(X0,X2),X1),
inference(unflattening,[status(thm)],[c_131]) ).
tcf(c_282,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_284,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_286,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_326,definition,
iPr_def_10 = multiply(x,x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_327,plain,
iPr_def_10 != x,
inference(demodulation,[status(thm)],[c_106,c_326]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(multiply(X0,X1),multiply(X0,X2)),add(multiply(X2,X1),multiply(X2,X2))) = add(multiply(X0,X1),X2),
inference(demodulation,[status(thm)],[c_280,c_284,c_286]) ).
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_282,c_284,c_286]) ).
tcf(c_468,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X0),X1) = add(X0,multiply(X1,X1)),
inference(superposition,[status(thm)],[c_437,c_403]) ).
tcf(c_488,plain,
! [X0: $i] : add(multiply(X0,X0),x) = add(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_326,c_468]) ).
tcf(c_519,plain,
! [X0: $i] : add(x,multiply(X0,X0)) = add(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_488,c_276]) ).
tcf(c_630,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = multiply(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_134,c_286]) ).
tcf(c_661,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = X0,
inference(light_normalisation,[status(thm)],[c_630,c_116]) ).
tcf(c_736,plain,
! [X0: $i] : add(multiply(X0,X0),additive_identity) = X0,
inference(superposition,[status(thm)],[c_136,c_661]) ).
tcf(c_770,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_736,c_114]) ).
tcf(c_771,plain,
! [X0: $i] : add(X0,iPr_def_10) = add(x,X0),
inference(demodulation,[status(thm)],[c_519,c_770]) ).
tcf(c_930,plain,
add(additive_identity,iPr_def_10) = x,
inference(superposition,[status(thm)],[c_771,c_114]) ).
tcf(c_940,plain,
add(additive_identity,iPr_def_10) != iPr_def_10,
inference(demodulation,[status(thm)],[c_327,c_930]) ).
tcf(c_941,plain,
$false,
inference(ground_joinability,[status(thm)],[c_940,c_113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 06:30:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 0.71/1.28 % SZS status Started for theBenchmark.p
% 0.71/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 0.71/1.28
% 0.71/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.71/1.28
% 0.71/1.28 % ------ iProver source info
% 0.71/1.28
% 0.71/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.71/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.71/1.28 % git: non_committed_changes: false
% 0.71/1.28
% 0.71/1.28 % ------ Parsing...% successful
% 0.71/1.28
% 0.71/1.28
% 0.71/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.71/1.28
% 0.71/1.28 % ------ 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 %
% 0.71/1.28
% 0.71/1.28 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 0.71/1.28 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.71/1.28
% 0.71/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 0.71/1.28 % ------ Proving...
% 0.71/1.28 % ------ Problem Properties
% 0.71/1.28
% 0.71/1.28 %
% 0.71/1.28 % clauses 14
% 0.71/1.28 % conjectures 0
% 0.71/1.28 % EPR 1
% 0.71/1.28 % Horn 14
% 0.71/1.28 % unary 14
% 0.71/1.28 % binary 0
% 0.71/1.28 % lits 14
% 0.71/1.28 % lits eq 14
% 0.71/1.28 % fd_pure 0
% 0.71/1.28 % fd_pseudo 0
% 0.71/1.28 % fd_cond 0
% 0.71/1.28 % fd_pseudo_cond 0
% 0.71/1.28 % AC symbols 0
% 0.71/1.28
% 0.71/1.28 % ------ Schedule UEQ
% 0.71/1.28
% 0.71/1.28 % ------ Option_UEQ Time Limit: 10.
% 0.71/1.28
% 0.71/1.28
% 0.71/1.28 % ------
% 0.71/1.28 % Current options:
% 0.71/1.28 % ------
% 0.71/1.28
% 0.71/1.28
% 0.71/1.28 %
% 0.71/1.28
% 0.71/1.28 % ------ Proving...
% 0.71/1.28 %
% 0.71/1.28
% 0.71/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 0.71/1.28
% 0.71/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.71/1.28
% 0.71/1.28
%------------------------------------------------------------------------------