%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO010-1 : 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 : n014.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 01:00:11 PM UTC 2026
% Result : Unsatisfiable 3.24s 1.15s
% Output : CNFRefutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 51 unt; 2 def)
% Number of atoms : 207 ( 57 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 89 ( 47 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 137 ( 0 sgn 137 !; 0 ?; 105 :)
% 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(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(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,
~ sum(x,multiply(x,y),x),
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_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(X6,X2,X5)
| ~ product(X6,X1,X4)
| ~ product(X6,X0,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sum(X0,X5,X6)
| ~ product(X2,X4,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(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(X5,X1,X6)
| ~ product(X2,X4,X6)
| ~ product(X0,X3,X5)
| ~ sum(X3,X1,X4)
| ~ sum(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,
~ sum(x,multiply(x,y),x),
inference(cnf_transformation,[],[f23]) ).
tcf(c_106,plain,
add(x,multiply(x,y)) != 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_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_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(X0,X5) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X1,X3) != X5 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_81]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( add(X6,X2) = X5 )
| ( add(X6,X1) != X4 )
| ( add(X6,X0) != X3 )
| ( multiply(X3,X4) != X5 )
| ( multiply(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(X2,X6) = X5 )
| ( add(X1,X6) != X4 )
| ( add(X0,X6) != X3 )
| ( multiply(X3,X4) != X5 )
| ( multiply(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_274,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(unflattening,[status(thm)],[c_111]) ).
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_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,y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_327,definition,
iPr_def_11 = add(x,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_328,plain,
iPr_def_11 != x,
inference(demodulation,[status(thm)],[c_106,c_326,c_327]) ).
tcf(c_384,plain,
add(iPr_def_10,x) = iPr_def_11,
inference(demodulation,[status(thm)],[c_327,c_276]) ).
tcf(c_415,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X2,X1)) = add(X1,multiply(X0,X2)),
inference(superposition,[status(thm)],[c_280,c_276]) ).
tcf(c_492,plain,
! [X0: $i] : multiply(add(X0,x),add(X0,y)) = add(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_326,c_282]) ).
tcf(c_497,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),add(X0,inverse(X1))) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_136,c_282]) ).
tcf(c_513,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),add(X0,inverse(X1))) = X0,
inference(light_normalisation,[status(thm)],[c_497,c_114]) ).
tcf(c_517,plain,
multiply(x,add(additive_identity,y)) = add(additive_identity,iPr_def_10),
inference(superposition,[status(thm)],[c_113,c_492]) ).
tcf(c_589,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(add(X0,X0),add(X0,X1)),multiply(add(X2,X0),add(X2,X1))) = multiply(X0,add(X2,X1)),
inference(demodulation,[status(thm)],[c_286,c_280,c_282]) ).
tcf(c_597,plain,
! [X0: $i] : multiply(add(x,iPr_def_10),multiply(add(X0,x),add(X0,y))) = multiply(x,add(X0,y)),
inference(superposition,[status(thm)],[c_492,c_589]) ).
tcf(c_647,plain,
! [X0: $i] : multiply(add(x,iPr_def_10),add(X0,iPr_def_10)) = multiply(x,add(X0,y)),
inference(light_normalisation,[status(thm)],[c_597,c_492]) ).
tcf(c_657,plain,
multiply(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_517,c_113,c_114,c_274,c_282,c_384,c_415,c_647]) ).
tcf(c_658,plain,
! [X0: $i] : multiply(add(iPr_def_10,X0),add(iPr_def_11,X0)) = add(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_657,c_280]) ).
tcf(c_667,plain,
! [X0: $i] : multiply(X0,add(additive_identity,inverse(X0))) = additive_identity,
inference(superposition,[status(thm)],[c_113,c_513]) ).
tcf(c_679,plain,
! [X0: $i] : multiply(add(X0,X0),multiplicative_identity) = X0,
inference(superposition,[status(thm)],[c_134,c_513]) ).
tcf(c_686,plain,
! [X0: $i,X1: $i] : multiply(multiply(add(X0,X0),add(X0,inverse(X0))),X1) = multiply(X0,add(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_513,c_589]) ).
tcf(c_694,plain,
! [X0: $i,X1: $i] : multiply(multiply(add(X0,X0),multiplicative_identity),X1) = multiply(X0,add(X1,inverse(X0))),
inference(light_normalisation,[status(thm)],[c_686,c_134]) ).
tcf(c_703,plain,
! [X0: $i] : add(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_679,c_116]) ).
tcf(c_762,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(demodulation,[status(thm)],[c_667,c_116,c_274,c_694,c_703]) ).
tcf(c_767,plain,
! [X0: $i,X1: $i] : multiply(add(additive_identity,X0),add(X1,X0)) = add(additive_identity,X0),
inference(superposition,[status(thm)],[c_762,c_280]) ).
tcf(c_770,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_767,c_113]) ).
tcf(c_1070,plain,
! [X0: $i] : multiply(add(x,X0),add(y,X0)) = add(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_326,c_415]) ).
tcf(c_1085,plain,
! [X0: $i] : multiply(add(iPr_def_10,X0),add(iPr_def_11,X0)) = add(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_657,c_415]) ).
tcf(c_1165,plain,
multiply(x,add(y,x)) = add(x,iPr_def_10),
inference(superposition,[status(thm)],[c_703,c_1070]) ).
tcf(c_1218,plain,
x = iPr_def_11,
inference(demodulation,[status(thm)],[c_1165,c_384,c_658,c_770,c_1085]) ).
tcf(c_1232,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_328,c_1218]) ).
tcf(c_1233,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_1232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.45 % Computer : n014.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Fri Sep 25 06:29:47 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 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
% 0.23/0.50
% 0.23/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.50
% 0.23/0.51 % Detected problem language: tptp
% 0.23/0.52 % Proving...
% 3.24/1.15 % SZS status Started for theBenchmark.p
% 3.24/1.15 % SZS status Unsatisfiable for theBenchmark.p
% 3.24/1.15
% 3.24/1.15 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.24/1.15
% 3.24/1.15 % ------ iProver source info
% 3.24/1.15
% 3.24/1.15 % git: date: 2026-07-19 20:42:38 +0200
% 3.24/1.15 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.24/1.15 % git: non_committed_changes: false
% 3.24/1.15
% 3.24/1.15 % ------ Parsing...% successful
% 3.24/1.15
% 3.24/1.15
% 3.24/1.15 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.24/1.15
% 3.24/1.15 % ------ 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 %
% 3.24/1.15
% 3.24/1.15 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.24/1.15 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.24/1.15
% 3.24/1.15 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.24/1.15 % ------ Proving...
% 3.24/1.15 % ------ Problem Properties
% 3.24/1.15
% 3.24/1.15 %
% 3.24/1.15 % clauses 15
% 3.24/1.15 % conjectures 0
% 3.24/1.15 % EPR 1
% 3.24/1.15 % Horn 15
% 3.24/1.15 % unary 15
% 3.24/1.15 % binary 0
% 3.24/1.15 % lits 15
% 3.24/1.15 % lits eq 15
% 3.24/1.15 % fd_pure 0
% 3.24/1.15 % fd_pseudo 0
% 3.24/1.15 % fd_cond 0
% 3.24/1.15 % fd_pseudo_cond 0
% 3.24/1.15 % AC symbols 0
% 3.24/1.15
% 3.24/1.15 % ------ Schedule UEQ
% 3.24/1.15
% 3.24/1.15 % ------ Option_UEQ Time Limit: 10.
% 3.24/1.15
% 3.24/1.15
% 3.24/1.15 % ------
% 3.24/1.15 % Current options:
% 3.24/1.15 % ------
% 3.24/1.15
% 3.24/1.15
% 3.24/1.15 %
% 3.24/1.15
% 3.24/1.15 % ------ Proving...
% 3.24/1.15 %
% 3.24/1.15
% 3.24/1.15 % SZS status Unsatisfiable for theBenchmark.p
% 3.24/1.15
% 3.24/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.24/1.16
% 3.24/1.16
%------------------------------------------------------------------------------