%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 01:37:05 PM UTC 2026
% Result : Unsatisfiable 19.05s 12.94s
% Output : Proof 19.05s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t13,axiom,
sFlat0 = less_equal(aQc,bQc),
introduced(definition) ).
cnf(t75,plain,
less_equal(aQc,bQc) = sFlat0,
inference(orient,[status(thm)],[t13]) ).
cnf(f1,axiom,
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
fof(f1_nnf,plain,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t9,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t51,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(f7,axiom,
quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
fof(f7_nnf,plain,
! [X,Y] : quotient(X,Y,divide(X,Y)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] : quotient(X,Y,divide(X,Y)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t6,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t18,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(f5,axiom,
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f5_nnf,plain,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t10,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t17,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(f4,axiom,
less_equal(zero,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f4_nnf,plain,
! [X] : less_equal(zero,X),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] : less_equal(zero,X),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
less_equal(zero,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t2,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t61,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t66,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t17,t61]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t2478,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t66,t14]) ).
cnf(t156,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t2478]) ).
cnf(f3,axiom,
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
fof(f3_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( less_equal(X6,X7)
| ~ quotient(X2,X3,X7)
| ~ quotient(X5,X4,X6)
| ~ quotient(X0,X3,X5)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t12,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X2,X4,X5),true,ifeq(quotient(X1,X4,X6),true,ifeq(quotient(X6,X5,X7),true,ifeq(quotient(X3,X4,X8),true,less_equal(X7,X8),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t27,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X2,X4,X5),true,ifeq(quotient(X1,X4,X6),true,ifeq(quotient(X6,X5,X7),true,ifeq(quotient(X3,X4,X8),true,less_equal(X7,X8),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(f11,hypothesis,
quotient(b,c,bQc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bQc) ).
fof(f11_nnf,plain,
quotient(b,c,bQc),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
quotient(b,c,bQc),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(t4,plain,
quotient(b,c,bQc) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t24,plain,
quotient(b,c,bQc) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t32,plain,
true = ifeq(quotient(X1,b,X2),true,ifeq(true,true,ifeq(quotient(X1,c,X3),true,ifeq(quotient(X3,bQc,X4),true,ifeq(quotient(X2,c,X5),true,less_equal(X4,X5),true),true),true),true),true),
inference(cp,[status(thm)],[t27,t24]) ).
cnf(t2567,plain,
true = ifeq(quotient(X1,b,X2),true,ifeq(quotient(X1,c,X3),true,ifeq(quotient(X3,bQc,X4),true,ifeq(quotient(X2,c,X5),true,less_equal(X4,X5),true),true),true),true),
inference(step,[status(thm)],[t32,t14]) ).
cnf(t1296,plain,
ifeq(quotient(X1,b,X2),true,ifeq(quotient(X1,c,X3),true,ifeq(quotient(X3,bQc,X4),true,ifeq(quotient(X2,c,X5),true,less_equal(X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t2567]) ).
cnf(f0,axiom,
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).
fof(f0_nnf,plain,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t7,plain,
ifeq(less_equal(X1,X2),true,quotient(X1,X2,zero),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t53,plain,
ifeq(less_equal(X1,X2),true,quotient(X1,X2,zero),true) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f9,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aLEb) ).
fof(f9_nnf,plain,
less_equal(a,b),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
less_equal(a,b),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(t1,plain,
less_equal(a,b) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t68,plain,
less_equal(a,b) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t69,plain,
true = ifeq(true,true,quotient(a,b,zero),true),
inference(cp,[status(thm)],[t53,t68]) ).
cnf(t2469,plain,
true = quotient(a,b,zero),
inference(step,[status(thm)],[t69,t14]) ).
cnf(t112,plain,
quotient(a,b,zero) = true,
inference(orient,[status(thm)],[t2469]) ).
cnf(t1301,plain,
true = ifeq(true,true,ifeq(quotient(a,c,X1),true,ifeq(quotient(X1,bQc,X2),true,ifeq(quotient(zero,c,X3),true,less_equal(X2,X3),true),true),true),true),
inference(cp,[status(thm)],[t1296,t112]) ).
cnf(t2699,plain,
true = ifeq(quotient(a,c,X1),true,ifeq(quotient(X1,bQc,X2),true,ifeq(quotient(zero,c,X3),true,less_equal(X2,X3),true),true),true),
inference(step,[status(thm)],[t1301,t14]) ).
cnf(t2209,plain,
ifeq(quotient(a,c,X1),true,ifeq(quotient(X1,bQc,X2),true,ifeq(quotient(zero,c,X3),true,less_equal(X2,X3),true),true),true) = true,
inference(orient,[status(thm)],[t2699]) ).
cnf(f10,hypothesis,
quotient(a,c,aQc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aQc) ).
fof(f10_nnf,plain,
quotient(a,c,aQc),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
quotient(a,c,aQc),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(t3,plain,
quotient(a,c,aQc) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t21,plain,
quotient(a,c,aQc) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t2210,plain,
true = ifeq(true,true,ifeq(quotient(aQc,bQc,X1),true,ifeq(quotient(zero,c,X2),true,less_equal(X1,X2),true),true),true),
inference(cp,[status(thm)],[t2209,t21]) ).
cnf(t2700,plain,
true = ifeq(quotient(aQc,bQc,X1),true,ifeq(quotient(zero,c,X2),true,less_equal(X1,X2),true),true),
inference(step,[status(thm)],[t2210,t14]) ).
cnf(t2216,plain,
ifeq(quotient(aQc,bQc,X1),true,ifeq(quotient(zero,c,X2),true,less_equal(X1,X2),true),true) = true,
inference(orient,[status(thm)],[t2700]) ).
cnf(t62,plain,
true = ifeq(true,true,quotient(zero,X1,zero),true),
inference(cp,[status(thm)],[t53,t61]) ).
cnf(t2468,plain,
true = quotient(zero,X1,zero),
inference(step,[status(thm)],[t62,t14]) ).
cnf(t104,plain,
quotient(zero,X1,zero) = true,
inference(orient,[status(thm)],[t2468]) ).
cnf(t2218,plain,
true = ifeq(quotient(aQc,bQc,X1),true,ifeq(true,true,less_equal(X1,zero),true),true),
inference(cp,[status(thm)],[t2216,t104]) ).
cnf(t2701,plain,
true = ifeq(quotient(aQc,bQc,X1),true,less_equal(X1,zero),true),
inference(step,[status(thm)],[t2218,t14]) ).
cnf(t2221,plain,
ifeq(quotient(aQc,bQc,X1),true,less_equal(X1,zero),true) = true,
inference(orient,[status(thm)],[t2701]) ).
cnf(t2222,plain,
true = ifeq(true,true,less_equal(divide(aQc,bQc),zero),true),
inference(cp,[status(thm)],[t2221,t18]) ).
cnf(t2702,plain,
true = less_equal(divide(aQc,bQc),zero),
inference(step,[status(thm)],[t2222,t14]) ).
cnf(t2223,plain,
less_equal(divide(aQc,bQc),zero) = true,
inference(orient,[status(thm)],[t2702]) ).
cnf(t2224,plain,
zero = ifeq(true,true,divide(aQc,bQc),zero),
inference(cp,[status(thm)],[t156,t2223]) ).
cnf(t2703,plain,
zero = divide(aQc,bQc),
inference(step,[status(thm)],[t2224,t14]) ).
cnf(t2229,plain,
divide(aQc,bQc) = zero,
inference(orient,[status(thm)],[t2703]) ).
cnf(t2230,plain,
true = quotient(aQc,bQc,zero),
inference(cp,[status(thm)],[t18,t2229]) ).
cnf(t2238,plain,
quotient(aQc,bQc,zero) = true,
inference(orient,[status(thm)],[t2230]) ).
cnf(t2240,plain,
true = ifeq(true,true,less_equal(aQc,bQc),true),
inference(cp,[status(thm)],[t51,t2238]) ).
cnf(t2707,plain,
true = less_equal(aQc,bQc),
inference(step,[status(thm)],[t2240,t14]) ).
cnf(t2708,plain,
true = sFlat0,
inference(step,[status(thm)],[t2707,t75]) ).
cnf(t2260,plain,
true = sFlat0,
inference(orient,[status(thm)],[t2708]) ).
cnf(f12,negated_conjecture,
~ less_equal(aQc,bQc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_aQcLEbQc) ).
fof(f12_nnf,plain,
~ less_equal(aQc,bQc),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ less_equal(aQc,bQc),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ less_equal(aQc,bQc),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(aQc,bQc) != true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
sFlat0 != true,
inference(rw,[status(thm)],[goal_0,t75]) ).
cnf(g0_1,plain,
sFlat0 != sFlat0,
inference(rw,[status(thm)],[g0_0,t2260]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/10.40 % Computer : n006.cluster.edu
% 0.03/10.40 % Model : x86_64 x86_64
% 0.03/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.40 % Memory : 8046.5625MB
% 0.03/10.40 % OS : Linux 6.8.0-71-generic
% 0.03/10.40 % CPULimit : 300
% 0.03/10.40 % WCLimit : 300
% 0.03/10.40 % DateTime : Wed Sep 23 16:14:11 UTC 2026
% 0.03/10.40 % CPUTime :
% 0.03/10.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 19.05/12.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.05/12.94 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------