%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 02:18:32 PM UTC 2026
% Result : Unsatisfiable 42.26s 6.71s
% Output : Proof 42.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 13
% Syntax : Number of formulae : 170 ( 138 unt; 0 def)
% Number of atoms : 226 ( 131 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 122 ( 66 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 309 ( 10 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f14,negated_conjecture,
( ~ divides(A,b)
| ~ divides(A,c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_no_common_divisor) ).
fof(f14_nnf,plain,
! [A] :
( ~ divides(A,b)
| ~ divides(A,c) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A] :
( ~ divides(A,b)
| ~ divides(A,c) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ divides(X0,b)
| ~ divides(X0,c) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t248,plain,
ifeq(divides(X1,c),true,ifeq(divides(X1,b),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t1043,plain,
ifeq(divides(X1,c),true,ifeq(divides(X1,b),true,false,true),true) = true,
inference(orient,[status(thm)],[t248]) ).
cnf(f8,axiom,
( divides(A,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_divisible_by_operand) ).
fof(f8_nnf,plain,
! [A,B,C] :
( divides(A,C)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] :
( divides(A,C)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( divides(X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(product(X0,X1,X2),true,divides(X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f0,axiom,
product(A,B,multiply(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product) ).
fof(f0_nnf,plain,
! [A,B] : product(A,B,multiply(A,B)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : product(A,B,multiply(A,B)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t9,plain,
divides(X1,multiply(X1,X2)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi0]) ).
cnf(t415,plain,
divides(X1,multiply(X1,X2)) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(h0,plain,
divides(V0,multiply(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi0]) ).
cnf(f7,axiom,
( product(A,second_divided_by_1st(A,B),B)
| ~ divides(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divides_implies_product) ).
fof(f7_nnf,plain,
! [A,B] :
( product(A,second_divided_by_1st(A,B),B)
| ~ divides(A,B) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( product(A,second_divided_by_1st(A,B),B)
| ~ divides(A,B) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( product(X0,second_divided_by_1st(X0,X1),X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(divides(X0,X1),true,product(X0,second_divided_by_1st(X0,X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h22,plain,
product(V0,second_divided_by_1st(V0,multiply(V0,V1)),multiply(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi7,h0]) ).
cnf(f4,axiom,
( B = D
| ~ product(A,D,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f4_nnf,plain,
! [A,B,C,D] :
( B = D
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( B = D
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( X1 = X3
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X2),true,X1,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t36,plain,
second_divided_by_1st(X1,multiply(X1,X2)) = X2,
inference(hyper_resolution,[status(thm)],[hi4,hi0,h22]) ).
cnf(t256,plain,
second_divided_by_1st(X1,multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t36]) ).
cnf(f3,axiom,
( product(B,A,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_commutativity) ).
fof(f3_nnf,plain,
! [A,B,C] :
( product(B,A,C)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] :
( product(B,A,C)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(product(X0,X1,X2),true,product(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h1,plain,
product(V0,V1,multiply(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi0]) ).
cnf(f6,axiom,
( D = C
| ~ product(A,B,D)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined_product) ).
fof(f6_nnf,plain,
! [A,B,C,D] :
( D = C
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C,D] :
( D = C
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( X3 = X2
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,X3,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t26,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(hyper_resolution,[status(thm)],[hi6,hi0,h1]) ).
cnf(t262,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t26]) ).
cnf(t263,plain,
X1 = second_divided_by_1st(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t256,t262]) ).
cnf(t1047,plain,
second_divided_by_1st(X1,multiply(X2,X1)) = X2,
inference(orient,[status(thm)],[t263]) ).
cnf(f2,axiom,
( product(F,E,C)
| ~ product(F,D,A)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_associativity2) ).
fof(f2_nnf,plain,
! [A,B,C,D,E,F] :
( product(F,E,C)
| ~ product(F,D,A)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D,E,F] :
( product(F,E,C)
| ~ product(F,D,A)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( product(X5,X4,X2)
| ~ product(X5,X3,X0)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X3,X0),true,product(X5,X4,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h2,plain,
product(V0,multiply(V1,V2),multiply(multiply(V0,V1),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi0,hi0,hi0]) ).
cnf(h74,plain,
product(V0,multiply(multiply(multiply(V1,V2),V3),V4),multiply(multiply(V3,V4),multiply(multiply(V0,V1),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi2,h1,h2,h2]) ).
cnf(t253,plain,
second_divided_by_1st(multiply(X1,X2),multiply(multiply(X1,X2),multiply(multiply(multiply(X1,X2),X3),X4))) = multiply(multiply(multiply(X3,X4),X1),X2),
inference(hyper_resolution,[status(thm)],[hi4,h22,h74]) ).
cnf(t12594,plain,
multiply(multiply(multiply(X1,X2),X3),X4) = multiply(multiply(multiply(X3,X4),X1),X2),
inference(step,[status(thm)],[t253,t256]) ).
cnf(t296,plain,
multiply(multiply(multiply(X1,X2),X3),X4) = multiply(multiply(multiply(X3,X4),X1),X2),
inference(orient,[status(thm)],[t12594]) ).
cnf(t299,plain,
multiply(multiply(multiply(X1,X2),X3),X4) = multiply(X2,multiply(multiply(X3,X4),X1)),
inference(cp,[status(thm)],[t296,t262]) ).
cnf(t3405,plain,
multiply(multiply(multiply(X1,X2),X3),X4) = multiply(X2,multiply(multiply(X3,X4),X1)),
inference(orient,[status(thm)],[t299]) ).
cnf(t3413,plain,
multiply(X1,multiply(multiply(X2,X3),X4)) = multiply(multiply(X2,multiply(X4,X1)),X3),
inference(cp,[status(thm)],[t3405,t262]) ).
cnf(t4680,plain,
multiply(multiply(X1,multiply(X2,X3)),X4) = multiply(X3,multiply(multiply(X1,X4),X2)),
inference(orient,[status(thm)],[t3413]) ).
cnf(f12,hypothesis,
product(c,c,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_squared) ).
fof(f12_nnf,plain,
product(c,c,e),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
product(c,c,e),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi12,axiom,
product(c,c,e) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h16,plain,
product(V0,e,multiply(multiply(V0,c),c)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi0,hi12,hi0]) ).
cnf(t124,plain,
multiply(multiply(X1,c),c) = multiply(X1,e),
inference(hyper_resolution,[status(thm)],[hi6,hi0,h16]) ).
cnf(t12592,plain,
multiply(c,multiply(X1,c)) = multiply(X1,e),
inference(step,[status(thm)],[t124,t262]) ).
cnf(t282,plain,
multiply(c,multiply(X1,c)) = multiply(X1,e),
inference(orient,[status(thm)],[t12592]) ).
cnf(t4692,plain,
multiply(c,multiply(multiply(c,X1),X2)) = multiply(multiply(X2,e),X1),
inference(cp,[status(thm)],[t4680,t282]) ).
cnf(t5,plain,
multiply(c,c) = e,
inference(hyper_resolution,[status(thm)],[hi6,hi0,hi12]) ).
cnf(t326,plain,
multiply(c,c) = e,
inference(orient,[status(thm)],[t5]) ).
cnf(t328,plain,
multiply(multiply(multiply(X1,X2),c),c) = multiply(multiply(e,X1),X2),
inference(cp,[status(thm)],[t296,t326]) ).
cnf(t12639,plain,
multiply(c,multiply(multiply(X1,X2),c)) = multiply(multiply(e,X1),X2),
inference(step,[status(thm)],[t328,t262]) ).
cnf(t12640,plain,
multiply(multiply(X1,X2),e) = multiply(multiply(e,X1),X2),
inference(step,[status(thm)],[t12639,t282]) ).
cnf(t12641,plain,
multiply(e,multiply(X1,X2)) = multiply(multiply(e,X1),X2),
inference(step,[status(thm)],[t12640,t262]) ).
cnf(t1788,plain,
multiply(multiply(e,X1),X2) = multiply(e,multiply(X1,X2)),
inference(orient,[status(thm)],[t12641]) ).
cnf(t1791,plain,
multiply(e,multiply(X1,X2)) = multiply(multiply(X1,e),X2),
inference(cp,[status(thm)],[t1788,t262]) ).
cnf(t1908,plain,
multiply(multiply(X1,e),X2) = multiply(e,multiply(X1,X2)),
inference(orient,[status(thm)],[t1791]) ).
cnf(t12683,plain,
multiply(c,multiply(multiply(c,X1),X2)) = multiply(e,multiply(X2,X1)),
inference(step,[status(thm)],[t4692,t1908]) ).
cnf(t4892,plain,
multiply(c,multiply(multiply(c,X1),X2)) = multiply(e,multiply(X2,X1)),
inference(orient,[status(thm)],[t12683]) ).
cnf(t4898,plain,
multiply(e,multiply(X1,X2)) = multiply(c,multiply(X1,multiply(c,X2))),
inference(cp,[status(thm)],[t4892,t262]) ).
cnf(t5683,plain,
multiply(c,multiply(X1,multiply(c,X2))) = multiply(e,multiply(X1,X2)),
inference(orient,[status(thm)],[t4898]) ).
cnf(t5706,plain,
multiply(X1,multiply(c,X2)) = second_divided_by_1st(c,multiply(e,multiply(X1,X2))),
inference(cp,[status(thm)],[t256,t5683]) ).
cnf(t285,plain,
multiply(X1,c) = second_divided_by_1st(c,multiply(X1,e)),
inference(cp,[status(thm)],[t256,t282]) ).
cnf(t1057,plain,
second_divided_by_1st(c,multiply(X1,e)) = multiply(X1,c),
inference(orient,[status(thm)],[t285]) ).
cnf(t1058,plain,
multiply(X1,c) = second_divided_by_1st(c,multiply(e,X1)),
inference(cp,[status(thm)],[t1057,t262]) ).
cnf(t1063,plain,
second_divided_by_1st(c,multiply(e,X1)) = multiply(X1,c),
inference(orient,[status(thm)],[t1058]) ).
cnf(t12691,plain,
multiply(X1,multiply(c,X2)) = multiply(multiply(X1,X2),c),
inference(step,[status(thm)],[t5706,t1063]) ).
cnf(t12692,plain,
multiply(X1,multiply(c,X2)) = multiply(c,multiply(X1,X2)),
inference(step,[status(thm)],[t12691,t262]) ).
cnf(t5780,plain,
multiply(X1,multiply(c,X2)) = multiply(c,multiply(X1,X2)),
inference(orient,[status(thm)],[t12692]) ).
cnf(t5805,plain,
X1 = second_divided_by_1st(multiply(c,X2),multiply(c,multiply(X1,X2))),
inference(cp,[status(thm)],[t1047,t5780]) ).
cnf(t10004,plain,
second_divided_by_1st(multiply(c,X1),multiply(c,multiply(X2,X1))) = X2,
inference(orient,[status(thm)],[t5805]) ).
cnf(t10034,plain,
X1 = second_divided_by_1st(multiply(c,X2),multiply(c,multiply(X2,X1))),
inference(cp,[status(thm)],[t10004,t262]) ).
cnf(t11428,plain,
second_divided_by_1st(multiply(c,X1),multiply(c,multiply(X1,X2))) = X2,
inference(orient,[status(thm)],[t10034]) ).
cnf(t5909,plain,
c = second_divided_by_1st(multiply(X1,X2),multiply(X1,multiply(c,X2))),
inference(cp,[status(thm)],[t1047,t5780]) ).
cnf(t10113,plain,
second_divided_by_1st(multiply(X1,X2),multiply(X1,multiply(c,X2))) = c,
inference(orient,[status(thm)],[t5909]) ).
cnf(t10129,plain,
c = second_divided_by_1st(multiply(X1,X2),multiply(X2,multiply(c,X1))),
inference(cp,[status(thm)],[t10113,t262]) ).
cnf(t11486,plain,
second_divided_by_1st(multiply(X1,X2),multiply(X2,multiply(c,X1))) = c,
inference(orient,[status(thm)],[t10129]) ).
cnf(t250,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X4,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t260,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X4,X3),X3) = X3,
inference(orient,[status(thm)],[t250]) ).
cnf(t42,plain,
product(X1,X2,multiply(X2,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi0]) ).
cnf(t331,plain,
product(X1,X2,multiply(X2,X1)) = true,
inference(orient,[status(thm)],[t42]) ).
cnf(t342,plain,
multiply(X1,X2) = ifeq(true,true,ifeq(product(X2,X1,X3),true,X3,multiply(X1,X2)),multiply(X1,X2)),
inference(cp,[status(thm)],[t260,t331]) ).
cnf(t25,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t257,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t25]) ).
cnf(t12731,plain,
multiply(X1,X2) = ifeq(product(X2,X1,X3),true,X3,multiply(X1,X2)),
inference(step,[status(thm)],[t342,t257]) ).
cnf(t11615,plain,
ifeq(product(X1,X2,X3),true,X3,multiply(X2,X1)) = multiply(X2,X1),
inference(orient,[status(thm)],[t12731]) ).
cnf(t246,plain,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t656,plain,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t246]) ).
cnf(t247,plain,
ifeq(divides(X1,X2),true,product(X1,second_divided_by_1st(X1,X2),X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t804,plain,
ifeq(divides(X1,X2),true,product(X1,second_divided_by_1st(X1,X2),X2),true) = true,
inference(orient,[status(thm)],[t247]) ).
cnf(f9,axiom,
( divides(A,C)
| ~ prime(A)
| ~ product(C,C,B)
| ~ divides(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',primes_lemma1) ).
fof(f9_nnf,plain,
! [A,B,C] :
( divides(A,C)
| ~ prime(A)
| ~ product(C,C,B)
| ~ divides(A,B) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B,C] :
( divides(A,C)
| ~ prime(A)
| ~ product(C,C,B)
| ~ divides(A,B) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( divides(X0,X2)
| ~ prime(X0)
| ~ product(X2,X2,X1)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
ifeq(divides(X0,X1),true,ifeq(product(X2,X2,X1),true,ifeq(prime(X0),true,divides(X0,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(f10,hypothesis,
prime(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_prime) ).
fof(f10_nnf,plain,
prime(a),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
prime(a),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(hi10,axiom,
prime(a) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t1,plain,
divides(a,a) = true,
inference(hyper_resolution,[status(thm)],[hi9,h0,hi0,hi10]) ).
cnf(t655,plain,
divides(a,a) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t807,plain,
true = ifeq(true,true,product(a,second_divided_by_1st(a,a),a),true),
inference(cp,[status(thm)],[t804,t655]) ).
cnf(t12611,plain,
true = product(a,second_divided_by_1st(a,a),a),
inference(step,[status(thm)],[t807,t257]) ).
cnf(t1065,plain,
product(a,second_divided_by_1st(a,a),a) = true,
inference(orient,[status(thm)],[t12611]) ).
cnf(t1066,plain,
true = ifeq(true,true,product(second_divided_by_1st(a,a),a,a),true),
inference(cp,[status(thm)],[t656,t1065]) ).
cnf(t12612,plain,
true = product(second_divided_by_1st(a,a),a,a),
inference(step,[status(thm)],[t1066,t257]) ).
cnf(t1080,plain,
product(second_divided_by_1st(a,a),a,a) = true,
inference(orient,[status(thm)],[t12612]) ).
cnf(t11621,plain,
multiply(a,second_divided_by_1st(a,a)) = ifeq(true,true,a,multiply(a,second_divided_by_1st(a,a))),
inference(cp,[status(thm)],[t11615,t1080]) ).
cnf(t12732,plain,
multiply(a,second_divided_by_1st(a,a)) = a,
inference(step,[status(thm)],[t11621,t257]) ).
cnf(t11666,plain,
multiply(a,second_divided_by_1st(a,a)) = a,
inference(orient,[status(thm)],[t12732]) ).
cnf(t11669,plain,
c = second_divided_by_1st(a,multiply(second_divided_by_1st(a,a),multiply(c,a))),
inference(cp,[status(thm)],[t11486,t11666]) ).
cnf(t5798,plain,
multiply(c,X1) = second_divided_by_1st(X2,multiply(c,multiply(X2,X1))),
inference(cp,[status(thm)],[t256,t5780]) ).
cnf(t6306,plain,
second_divided_by_1st(X1,multiply(c,multiply(X1,X2))) = multiply(c,X2),
inference(orient,[status(thm)],[t5798]) ).
cnf(t6331,plain,
multiply(c,X1) = second_divided_by_1st(X2,multiply(c,multiply(X1,X2))),
inference(cp,[status(thm)],[t6306,t262]) ).
cnf(t6361,plain,
second_divided_by_1st(X1,multiply(c,multiply(X2,X1))) = multiply(c,X2),
inference(orient,[status(thm)],[t6331]) ).
cnf(t6369,plain,
multiply(c,X1) = second_divided_by_1st(X2,multiply(X1,multiply(c,X2))),
inference(cp,[status(thm)],[t6361,t5780]) ).
cnf(t6423,plain,
second_divided_by_1st(X1,multiply(X2,multiply(c,X1))) = multiply(c,X2),
inference(orient,[status(thm)],[t6369]) ).
cnf(t12733,plain,
c = multiply(c,second_divided_by_1st(a,a)),
inference(step,[status(thm)],[t11669,t6423]) ).
cnf(t11730,plain,
multiply(c,second_divided_by_1st(a,a)) = c,
inference(orient,[status(thm)],[t12733]) ).
cnf(t11731,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(c,c),
inference(cp,[status(thm)],[t256,t11730]) ).
cnf(t11828,plain,
second_divided_by_1st(a,a) = second_divided_by_1st(c,c),
inference(orient,[status(thm)],[t11731]) ).
cnf(t12734,plain,
multiply(c,second_divided_by_1st(c,c)) = c,
inference(step,[status(thm)],[t11730,t11828]) ).
cnf(t11830,plain,
multiply(c,second_divided_by_1st(c,c)) = c,
inference(rw,[status(thm)],[t12734]) ).
cnf(t11836,plain,
multiply(c,second_divided_by_1st(c,c)) = c,
inference(orient,[status(thm)],[t11830]) ).
cnf(t11854,plain,
second_divided_by_1st(c,c) = second_divided_by_1st(multiply(c,c),multiply(c,c)),
inference(cp,[status(thm)],[t11428,t11836]) ).
cnf(t12740,plain,
second_divided_by_1st(c,c) = second_divided_by_1st(e,multiply(c,c)),
inference(step,[status(thm)],[t11854,t326]) ).
cnf(t12741,plain,
second_divided_by_1st(c,c) = second_divided_by_1st(e,e),
inference(step,[status(thm)],[t12740,t326]) ).
cnf(t11922,plain,
second_divided_by_1st(c,c) = second_divided_by_1st(e,e),
inference(orient,[status(thm)],[t12741]) ).
cnf(t12744,plain,
multiply(c,second_divided_by_1st(e,e)) = c,
inference(step,[status(thm)],[t11836,t11922]) ).
cnf(t11926,plain,
multiply(c,second_divided_by_1st(e,e)) = c,
inference(rw,[status(thm)],[t12744]) ).
cnf(t12002,plain,
multiply(c,second_divided_by_1st(e,e)) = c,
inference(orient,[status(thm)],[t11926]) ).
cnf(t12019,plain,
X1 = second_divided_by_1st(c,multiply(c,multiply(second_divided_by_1st(e,e),X1))),
inference(cp,[status(thm)],[t11428,t12002]) ).
cnf(t12752,plain,
X1 = multiply(second_divided_by_1st(e,e),X1),
inference(step,[status(thm)],[t12019,t256]) ).
cnf(t12372,plain,
multiply(second_divided_by_1st(e,e),X1) = X1,
inference(orient,[status(thm)],[t12752]) ).
cnf(t12385,plain,
true = divides(second_divided_by_1st(e,e),X1),
inference(cp,[status(thm)],[t415,t12372]) ).
cnf(t12577,plain,
divides(second_divided_by_1st(e,e),X1) = true,
inference(orient,[status(thm)],[t12385]) ).
cnf(t12579,plain,
true = ifeq(true,true,ifeq(divides(second_divided_by_1st(e,e),b),true,false,true),true),
inference(cp,[status(thm)],[t1043,t12577]) ).
cnf(t12755,plain,
true = ifeq(divides(second_divided_by_1st(e,e),b),true,false,true),
inference(step,[status(thm)],[t12579,t257]) ).
cnf(t12756,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t12755,t12577]) ).
cnf(t12757,plain,
true = false,
inference(step,[status(thm)],[t12756,t257]) ).
cnf(t12587,plain,
false = true,
inference(orient,[status(thm)],[t12757]) ).
cnf(f13,hypothesis,
~ product(a,e,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_squared_is_not_b_squared) ).
fof(f13_nnf,plain,
~ product(a,e,d),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ product(a,e,d),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ product(a,e,d),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c13,c14]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t12587]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 02:40:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 42.26/6.71 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 42.26/6.71 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------