%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO007-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 01:00:09 PM UTC 2026
% Result : Unsatisfiable 68.67s 11.39s
% Output : CNFRefutation 68.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 17
% Syntax : Number of formulae : 170 ( 152 unt; 0 def)
% Number of atoms : 579 ( 155 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 110 ( 56 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 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 : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-1 aty)
% Number of variables : 241 ( 0 sgn 241 !; 0 ?; 201 :)
% 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(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,axiom,
product(y,z,y_times_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',y_times_z) ).
fof(f24,axiom,
product(x,y_times_z,x_times__y_times_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_times__y_times_z) ).
fof(f25,axiom,
product(x,y,x_times_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_times_y) ).
fof(f26,axiom,
product(x_times_y,z,x_times_y__times_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_times_y__times_z) ).
fof(f27,negated_conjecture,
x_times__y_times_z != x_times_y__times_z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equality) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
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_81,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_82,plain,
! [X0: $i] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_83,plain,
! [X0: $i] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[],[f8]) ).
tcf(c_85,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_87,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_89,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_91,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_93,plain,
! [X0: $i] : sum(X0,inverse(X0),multiplicative_identity),
inference(cnf_transformation,[],[f18]) ).
tcf(c_95,plain,
! [X0: $i] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[],[f20]) ).
tcf(c_98,plain,
product(y,z,y_times_z),
inference(cnf_transformation,[],[f23]) ).
tcf(c_99,plain,
product(x,y_times_z,x_times__y_times_z),
inference(cnf_transformation,[],[f24]) ).
tcf(c_100,plain,
product(x,y,x_times_y),
inference(cnf_transformation,[],[f25]) ).
tcf(c_101,plain,
product(x_times_y,z,x_times_y__times_z),
inference(cnf_transformation,[],[f26]) ).
tcf(c_102,negated_conjecture,
x_times__y_times_z != x_times_y__times_z,
inference(cnf_transformation,[],[f27]) ).
tcf(c_114,plain,
multiply(y,z) = y_times_z,
inference(well_definedness,[status(thm)],[c_98]) ).
tcf(c_115,plain,
multiply(x,y_times_z) = x_times__y_times_z,
inference(well_definedness,[status(thm)],[c_99]) ).
tcf(c_116,plain,
multiply(x,y) = x_times_y,
inference(well_definedness,[status(thm)],[c_100]) ).
tcf(c_117,plain,
multiply(x_times_y,z) = x_times_y__times_z,
inference(well_definedness,[status(thm)],[c_101]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_78]) ).
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_125,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(well_definedness,[status(thm)],[c_81]) ).
tcf(c_126,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_82]) ).
tcf(c_127,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(well_definedness,[status(thm)],[c_83]) ).
tcf(c_130,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_85]) ).
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_138,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_89]) ).
tcf(c_142,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_91]) ).
tcf(c_145,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(well_definedness,[status(thm)],[c_93]) ).
tcf(c_147,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_95]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(unflattening,[status(thm)],[c_122]) ).
tcf(c_294,plain,
multiply(y,x) = x_times_y,
inference(demodulation,[status(thm)],[c_116,c_293]) ).
tcf(c_295,plain,
multiply(y_times_z,x) = x_times__y_times_z,
inference(demodulation,[status(thm)],[c_115,c_293]) ).
tcf(c_296,plain,
multiply(z,x_times_y) = x_times_y__times_z,
inference(demodulation,[status(thm)],[c_117,c_293]) ).
tcf(c_298,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_120]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X2,X1)) = add(multiply(X0,X2),X1),
inference(unflattening,[status(thm)],[c_142]) ).
tcf(c_304,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_138]) ).
tcf(c_306,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_308,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_130]) ).
tcf(c_466,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(multiply(additive_identity,X1),X0),
inference(superposition,[status(thm)],[c_124,c_302]) ).
tcf(c_471,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),X1) = add(multiply(X0,additive_identity),X1),
inference(superposition,[status(thm)],[c_124,c_302]) ).
tcf(c_504,plain,
! [X0: $i] : add(multiply(additive_identity,additive_identity),X0) = multiply(X0,X0),
inference(superposition,[status(thm)],[c_124,c_466]) ).
tcf(c_507,plain,
! [X0: $i] : add(multiply(additive_identity,X0),multiplicative_identity) = add(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_466,c_126]) ).
tcf(c_530,plain,
! [X0: $i] : add(X0,multiply(additive_identity,additive_identity)) = multiply(X0,X0),
inference(superposition,[status(thm)],[c_504,c_298]) ).
tcf(c_1139,plain,
! [X0: $i,X1: $i] : add(add(X0,X1),multiply(additive_identity,additive_identity)) = add(X0,multiply(X1,X1)),
inference(superposition,[status(thm)],[c_304,c_530]) ).
tcf(c_1173,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(add(multiplicative_identity,X1),X0),
inference(superposition,[status(thm)],[c_126,c_306]) ).
tcf(c_3373,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(add(X1,multiplicative_identity),X0),
inference(superposition,[status(thm)],[c_298,c_1173]) ).
tcf(c_5519,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(add(X1,multiplicative_identity),X0),
inference(superposition,[status(thm)],[c_293,c_3373]) ).
tcf(c_5521,plain,
! [X0: $i] : multiply(add(multiplicative_identity,multiplicative_identity),X0) = add(X0,X0),
inference(superposition,[status(thm)],[c_126,c_3373]) ).
tcf(c_5595,plain,
! [X0: $i] : add(multiplicative_identity,multiply(additive_identity,X0)) = add(X0,multiplicative_identity),
inference(demodulation,[status(thm)],[c_507,c_298]) ).
tcf(c_5598,plain,
add(multiplicative_identity,additive_identity) = add(multiplicative_identity,multiplicative_identity),
inference(superposition,[status(thm)],[c_127,c_5595]) ).
tcf(c_5600,plain,
add(multiplicative_identity,multiplicative_identity) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_5598,c_125]) ).
tcf(c_5661,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),X0) = add(X0,multiply(X1,additive_identity)),
inference(superposition,[status(thm)],[c_125,c_304]) ).
tcf(c_5991,plain,
! [X0: $i] : add(X0,X0) = X0,
inference(light_normalisation,[status(thm)],[c_5521,c_126,c_5600]) ).
tcf(c_5999,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
inference(superposition,[status(thm)],[c_5991,c_304]) ).
tcf(c_8369,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = add(X0,multiply(X1,additive_identity)),
inference(demodulation,[status(thm)],[c_5661,c_293,c_5999]) ).
tcf(c_10087,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,additive_identity)) = multiply(add(X1,multiplicative_identity),X0),
inference(superposition,[status(thm)],[c_5519,c_8369]) ).
tcf(c_22496,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X2,X1)),
inference(superposition,[status(thm)],[c_304,c_293]) ).
tcf(c_26014,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,multiply(X1,X2)) = add(X0,multiply(X2,X1)),
inference(superposition,[status(thm)],[c_22496,c_304]) ).
tcf(c_43680,plain,
inverse(multiplicative_identity) = additive_identity,
inference(superposition,[status(thm)],[c_126,c_147]) ).
tcf(c_43714,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(multiply(X1,additive_identity),X0),
inference(demodulation,[status(thm)],[c_471,c_293]) ).
tcf(c_43716,plain,
! [X0: $i] : add(multiply(additive_identity,additive_identity),X0) = multiply(X0,X0),
inference(superposition,[status(thm)],[c_124,c_43714]) ).
tcf(c_43758,plain,
! [X0: $i] : add(multiplicative_identity,multiply(additive_identity,X0)) = add(X0,multiplicative_identity),
inference(demodulation,[status(thm)],[c_507,c_298]) ).
tcf(c_43763,plain,
add(multiplicative_identity,additive_identity) = add(multiplicative_identity,multiplicative_identity),
inference(superposition,[status(thm)],[c_127,c_43758]) ).
tcf(c_43770,plain,
add(multiplicative_identity,multiplicative_identity) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_43763,c_125]) ).
tcf(c_43789,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(multiply(additive_identity,X1),X0),
inference(superposition,[status(thm)],[c_124,c_302]) ).
tcf(c_43832,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[status(thm)],[c_145,c_304]) ).
tcf(c_43873,plain,
! [X0: $i] : add(y_times_z,multiply(X0,z)) = multiply(add(y,X0),z),
inference(superposition,[status(thm)],[c_114,c_306]) ).
tcf(c_43874,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X0)) = multiply(add(X1,X2),X0),
inference(superposition,[status(thm)],[c_293,c_306]) ).
tcf(c_43880,plain,
! [X0: $i] : add(x_times_y,multiply(X0,x)) = multiply(add(y,X0),x),
inference(superposition,[status(thm)],[c_294,c_306]) ).
tcf(c_43917,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X1,X2)) = multiply(X1,add(X0,X2)),
inference(superposition,[status(thm)],[c_293,c_308]) ).
tcf(c_43924,plain,
! [X0: $i] : add(x_times__y_times_z,multiply(y_times_z,X0)) = multiply(y_times_z,add(x,X0)),
inference(superposition,[status(thm)],[c_295,c_308]) ).
tcf(c_43925,plain,
! [X0: $i] : add(x_times_y__times_z,multiply(z,X0)) = multiply(z,add(x_times_y,X0)),
inference(superposition,[status(thm)],[c_296,c_308]) ).
tcf(c_44007,plain,
! [X0: $i] : add(y_times_z,multiply(z,X0)) = multiply(z,add(y,X0)),
inference(superposition,[status(thm)],[c_114,c_43917]) ).
tcf(c_44014,plain,
! [X0: $i] : add(x_times_y,multiply(x,X0)) = multiply(x,add(y,X0)),
inference(superposition,[status(thm)],[c_294,c_43917]) ).
tcf(c_44015,plain,
! [X0: $i] : add(x_times__y_times_z,multiply(x,X0)) = multiply(x,add(y_times_z,X0)),
inference(superposition,[status(thm)],[c_295,c_43917]) ).
tcf(c_44266,plain,
! [X0: $i] : multiply(add(multiplicative_identity,multiplicative_identity),X0) = add(X0,X0),
inference(superposition,[status(thm)],[c_126,c_1173]) ).
tcf(c_44280,plain,
! [X0: $i] : add(X0,multiply(additive_identity,X0)) = multiply(multiplicative_identity,X0),
inference(superposition,[status(thm)],[c_125,c_1173]) ).
tcf(c_44362,plain,
! [X0: $i] : add(inverse(add(X0,multiplicative_identity)),multiply(X0,additive_identity)) = additive_identity,
inference(superposition,[status(thm)],[c_10087,c_147]) ).
tcf(c_44436,plain,
! [X0: $i] : add(X0,X0) = X0,
inference(light_normalisation,[status(thm)],[c_44266,c_126,c_43770]) ).
tcf(c_44446,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
inference(superposition,[status(thm)],[c_44436,c_304]) ).
tcf(c_44470,plain,
! [X0: $i] : add(X0,multiply(additive_identity,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_44280,c_126]) ).
tcf(c_44487,plain,
! [X0: $i,X1: $i] : add(X0,multiply(multiply(additive_identity,X0),X1)) = multiply(X0,add(X0,X1)),
inference(superposition,[status(thm)],[c_44470,c_304]) ).
tcf(c_44489,plain,
! [X0: $i] : add(X0,multiply(multiply(additive_identity,X0),multiply(additive_identity,X0))) = add(X0,multiply(additive_identity,additive_identity)),
inference(superposition,[status(thm)],[c_44470,c_1139]) ).
tcf(c_44498,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_44470,c_530]) ).
tcf(c_44509,plain,
! [X0: $i] : add(X0,multiply(multiply(additive_identity,X0),multiply(additive_identity,X0))) = add(X0,additive_identity),
inference(light_normalisation,[status(thm)],[c_44489,c_44498]) ).
tcf(c_44510,plain,
! [X0: $i] : multiply(X0,X0) = add(X0,additive_identity),
inference(demodulation,[status(thm)],[c_44509,c_44470,c_44487]) ).
tcf(c_44511,plain,
! [X0: $i] : multiply(X0,X0) = add(additive_identity,X0),
inference(demodulation,[status(thm)],[c_43716,c_44498]) ).
tcf(c_44560,plain,
! [X0: $i] : add(multiply(X0,additive_identity),inverse(add(X0,multiplicative_identity))) = additive_identity,
inference(demodulation,[status(thm)],[c_44362,c_298]) ).
tcf(c_44563,plain,
! [X0: $i] : add(multiply(additive_identity,X0),inverse(add(X0,multiplicative_identity))) = additive_identity,
inference(superposition,[status(thm)],[c_293,c_44560]) ).
tcf(c_44722,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(light_normalisation,[status(thm)],[c_44510,c_125,c_44511]) ).
tcf(c_44739,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),X0) = multiply(add(X1,X0),X0),
inference(superposition,[status(thm)],[c_44722,c_43874]) ).
tcf(c_44905,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = add(multiply(additive_identity,X1),X0),
inference(demodulation,[status(thm)],[c_44739,c_293,c_298,c_43789]) ).
tcf(c_44950,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = add(multiply(additive_identity,X1),X0),
inference(superposition,[status(thm)],[c_44905,c_26014]) ).
tcf(c_44961,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = add(X0,multiply(additive_identity,X1)),
inference(superposition,[status(thm)],[c_44905,c_298]) ).
tcf(c_45453,plain,
! [X0: $i] : add(y_times_z,multiply(X0,z)) = multiply(z,add(y,X0)),
inference(demodulation,[status(thm)],[c_43873,c_293]) ).
tcf(c_45460,plain,
add(y_times_z,multiply(inverse(y),z)) = multiply(z,multiplicative_identity),
inference(superposition,[status(thm)],[c_145,c_45453]) ).
tcf(c_45513,plain,
add(y_times_z,multiply(z,inverse(y))) = z,
inference(demodulation,[status(thm)],[c_45460,c_127,c_26014]) ).
tcf(c_45707,plain,
! [X0: $i] : add(x_times_y,multiply(X0,x)) = multiply(x,add(y,X0)),
inference(demodulation,[status(thm)],[c_43880,c_293]) ).
tcf(c_45714,plain,
add(x_times_y,multiply(inverse(y),x)) = multiply(x,multiplicative_identity),
inference(superposition,[status(thm)],[c_145,c_45707]) ).
tcf(c_45774,plain,
add(x_times_y,multiply(x,inverse(y))) = x,
inference(demodulation,[status(thm)],[c_45714,c_127,c_26014]) ).
tcf(c_47195,plain,
add(x_times__y_times_z,multiply(y_times_z,inverse(x))) = multiply(y_times_z,multiplicative_identity),
inference(superposition,[status(thm)],[c_145,c_43924]) ).
tcf(c_47266,plain,
add(x_times__y_times_z,multiply(y_times_z,inverse(x))) = y_times_z,
inference(demodulation,[status(thm)],[c_47195,c_127]) ).
tcf(c_47285,plain,
! [X0: $i] : add(x_times_y__times_z,multiply(z,X0)) = multiply(z,add(X0,x_times_y)),
inference(superposition,[status(thm)],[c_298,c_43925]) ).
tcf(c_48989,plain,
add(y,multiply(additive_identity,z)) = add(y,y_times_z),
inference(superposition,[status(thm)],[c_114,c_44961]) ).
tcf(c_48996,plain,
add(y,multiply(additive_identity,x)) = add(y,x_times_y),
inference(superposition,[status(thm)],[c_294,c_44961]) ).
tcf(c_49253,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(demodulation,[status(thm)],[c_43832,c_126]) ).
tcf(c_49269,plain,
! [X0: $i] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_127,c_49253]) ).
tcf(c_49362,plain,
! [X0: $i] : add(X0,multiplicative_identity) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_49269,c_145]) ).
tcf(c_49363,plain,
! [X0: $i] : add(multiply(additive_identity,X0),inverse(multiplicative_identity)) = additive_identity,
inference(demodulation,[status(thm)],[c_44563,c_49362]) ).
tcf(c_49487,plain,
! [X0: $i] : add(multiply(additive_identity,X0),additive_identity) = additive_identity,
inference(light_normalisation,[status(thm)],[c_49363,c_43680]) ).
tcf(c_49488,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(demodulation,[status(thm)],[c_49487,c_124,c_44950]) ).
tcf(c_49510,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(superposition,[status(thm)],[c_49488,c_293]) ).
tcf(c_49551,plain,
add(y,y_times_z) = add(y,additive_identity),
inference(demodulation,[status(thm)],[c_48989,c_49510]) ).
tcf(c_49557,plain,
add(y,x_times_y) = add(y,additive_identity),
inference(demodulation,[status(thm)],[c_48996,c_49510]) ).
tcf(c_49565,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = add(X0,additive_identity),
inference(demodulation,[status(thm)],[c_44961,c_49510]) ).
tcf(c_49624,plain,
add(y,y_times_z) = y,
inference(demodulation,[status(thm)],[c_49551,c_125]) ).
tcf(c_49631,plain,
add(x_times_y,multiply(x,y_times_z)) = multiply(x,y),
inference(superposition,[status(thm)],[c_49624,c_44014]) ).
tcf(c_49658,plain,
add(y,x_times_y) = y,
inference(demodulation,[status(thm)],[c_49557,c_125]) ).
tcf(c_49666,plain,
add(y_times_z,multiply(z,x_times_y)) = multiply(z,y),
inference(superposition,[status(thm)],[c_49658,c_44007]) ).
tcf(c_49723,plain,
add(y_times_z,x_times_y__times_z) = multiply(z,y),
inference(light_normalisation,[status(thm)],[c_49666,c_296]) ).
tcf(c_49724,plain,
add(y_times_z,x_times_y__times_z) = y_times_z,
inference(demodulation,[status(thm)],[c_49723,c_114,c_293]) ).
tcf(c_49731,plain,
add(x_times__y_times_z,multiply(x,x_times_y__times_z)) = multiply(x,y_times_z),
inference(superposition,[status(thm)],[c_49724,c_44015]) ).
tcf(c_49742,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = X0,
inference(light_normalisation,[status(thm)],[c_49565,c_125]) ).
tcf(c_49743,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_44446,c_49742]) ).
tcf(c_49784,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,multiply(X1,multiply(X0,X2))) = multiply(add(X0,X1),X0),
inference(superposition,[status(thm)],[c_49742,c_304]) ).
tcf(c_49814,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_298,c_49743]) ).
tcf(c_49843,plain,
multiply(x_times__y_times_z,y_times_z) = x_times__y_times_z,
inference(superposition,[status(thm)],[c_47266,c_49743]) ).
tcf(c_49846,plain,
multiply(y_times_z,z) = y_times_z,
inference(superposition,[status(thm)],[c_45513,c_49743]) ).
tcf(c_49847,plain,
multiply(x_times_y,x) = x_times_y,
inference(superposition,[status(thm)],[c_45774,c_49743]) ).
tcf(c_49964,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,multiply(X1,multiply(X0,X2))) = X0,
inference(demodulation,[status(thm)],[c_49784,c_293,c_49743]) ).
tcf(c_50569,plain,
multiply(y_times_z,x_times__y_times_z) = x_times__y_times_z,
inference(demodulation,[status(thm)],[c_49843,c_293]) ).
tcf(c_50623,plain,
multiply(z,y_times_z) = y_times_z,
inference(demodulation,[status(thm)],[c_49846,c_293]) ).
tcf(c_50635,plain,
! [X0: $i] : add(z,multiply(X0,y_times_z)) = z,
inference(superposition,[status(thm)],[c_50623,c_49964]) ).
tcf(c_50651,plain,
multiply(x,x_times_y) = x_times_y,
inference(demodulation,[status(thm)],[c_49847,c_293]) ).
tcf(c_50663,plain,
! [X0: $i] : add(x,multiply(X0,x_times_y)) = x,
inference(superposition,[status(thm)],[c_50651,c_49964]) ).
tcf(c_52149,plain,
! [X0: $i] : add(z,multiply(y_times_z,X0)) = z,
inference(superposition,[status(thm)],[c_50635,c_26014]) ).
tcf(c_52176,plain,
add(x,x_times_y__times_z) = x,
inference(superposition,[status(thm)],[c_296,c_50663]) ).
tcf(c_52225,plain,
multiply(x_times_y__times_z,x) = x_times_y__times_z,
inference(superposition,[status(thm)],[c_52176,c_49814]) ).
tcf(c_52246,plain,
multiply(x,x_times_y__times_z) = x_times_y__times_z,
inference(demodulation,[status(thm)],[c_52225,c_293]) ).
tcf(c_53335,plain,
add(z,x_times__y_times_z) = z,
inference(superposition,[status(thm)],[c_50569,c_52149]) ).
tcf(c_53387,plain,
multiply(x_times__y_times_z,z) = x_times__y_times_z,
inference(superposition,[status(thm)],[c_53335,c_49814]) ).
tcf(c_53409,plain,
multiply(z,x_times__y_times_z) = x_times__y_times_z,
inference(demodulation,[status(thm)],[c_53387,c_293]) ).
tcf(c_54152,plain,
add(x_times__y_times_z,x_times_y) = x_times_y,
inference(demodulation,[status(thm)],[c_49631,c_293,c_294,c_295,c_298,c_26014]) ).
tcf(c_54388,plain,
add(x_times__y_times_z,x_times_y__times_z) = multiply(x,y_times_z),
inference(light_normalisation,[status(thm)],[c_49731,c_52246]) ).
tcf(c_54389,plain,
add(x_times__y_times_z,x_times_y__times_z) = x_times__y_times_z,
inference(demodulation,[status(thm)],[c_54388,c_293,c_295]) ).
tcf(c_63832,plain,
add(x_times_y__times_z,multiply(z,x_times__y_times_z)) = multiply(z,x_times_y),
inference(superposition,[status(thm)],[c_54152,c_47285]) ).
tcf(c_73496,plain,
add(x_times_y__times_z,x_times__y_times_z) = x_times_y__times_z,
inference(light_normalisation,[status(thm)],[c_63832,c_296,c_53409]) ).
tcf(c_73497,plain,
x_times__y_times_z = x_times_y__times_z,
inference(demodulation,[status(thm)],[c_73496,c_298,c_54389]) ).
tcf(c_73498,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_73497,c_102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO007-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 06:28:19 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 68.67/11.39 % SZS status Started for theBenchmark.p
% 68.67/11.39 % SZS status Unsatisfiable for theBenchmark.p
% 68.67/11.39
% 68.67/11.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 68.67/11.39
% 68.67/11.39 % ------ iProver source info
% 68.67/11.39
% 68.67/11.39 % git: date: 2026-07-19 20:42:38 +0200
% 68.67/11.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 68.67/11.39 % git: non_committed_changes: false
% 68.67/11.39
% 68.67/11.39 % ------ Parsing...% successful
% 68.67/11.39
% 68.67/11.39
% 68.67/11.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 68.67/11.39
% 68.67/11.39 % ------ Preprocessing... sup_sim: 21 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 %
% 68.67/11.39
% 68.67/11.39 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 68.67/11.39
% 68.67/11.39 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 68.67/11.39 % ------ Proving...
% 68.67/11.39 % ------ Problem Properties
% 68.67/11.39
% 68.67/11.39 %
% 68.67/11.39 % clauses 17
% 68.67/11.39 % conjectures 1
% 68.67/11.39 % EPR 1
% 68.67/11.39 % Horn 17
% 68.67/11.39 % unary 17
% 68.67/11.39 % binary 0
% 68.67/11.39 % lits 17
% 68.67/11.39 % lits eq 17
% 68.67/11.39 % fd_pure 0
% 68.67/11.39 % fd_pseudo 0
% 68.67/11.39 % fd_cond 0
% 68.67/11.39 % fd_pseudo_cond 0
% 68.67/11.39 % AC symbols 0
% 68.67/11.39
% 68.67/11.39 % ------ Input Options Time Limit: Unbounded
% 68.67/11.39
% 68.67/11.39
% 68.67/11.39 % ------
% 68.67/11.39 % Current options:
% 68.67/11.39 % ------
% 68.67/11.39
% 68.67/11.39
% 68.67/11.39 %
% 68.67/11.39
% 68.67/11.39 % ------ Proving...
% 68.67/11.39 %
% 68.67/11.39
% 68.67/11.39 % SZS status Unsatisfiable for theBenchmark.p
% 68.67/11.39
% 68.67/11.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 68.67/11.40
% 68.67/11.40
%------------------------------------------------------------------------------