%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO619+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 01:18:18 PM UTC 2026
% Result : Theorem 136.86s 20.22s
% Output : Proof 136.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 74
% Number of leaves : 28
% Syntax : Number of formulae : 310 ( 202 unt; 0 def)
% Number of atoms : 506 ( 198 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 316 ( 120 ~; 114 |; 54 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 15 ( 15 usr; 14 con; 0-4 aty)
% Number of variables : 1014 ( 83 sgn 432 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f94,conjecture,
! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ( circle(F,E,H,NWPNT4)
& coll(H,C,D)
& circle(F,E,G,NWPNT3)
& coll(G,C,E)
& circle(F,E,NWPNT1,NWPNT2)
& midp(F,D,E)
& coll(E,A,B)
& eqangle(E,C,C,A,A,C,C,D)
& coll(D,A,B)
& cong(A,C,B,C)
& perp(C,A,C,B) )
=> cong(D,G,D,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL8110981) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ( circle(F,E,H,NWPNT4)
& coll(H,C,D)
& circle(F,E,G,NWPNT3)
& coll(G,C,E)
& circle(F,E,NWPNT1,NWPNT2)
& midp(F,D,E)
& coll(E,A,B)
& eqangle(E,C,C,A,A,C,C,D)
& coll(D,A,B)
& cong(A,C,B,C)
& perp(C,A,C,B) )
=> cong(D,G,D,H) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ~ cong(D,G,D,H)
& circle(F,E,H,NWPNT4)
& coll(H,C,D)
& circle(F,E,G,NWPNT3)
& coll(G,C,E)
& circle(F,E,NWPNT1,NWPNT2)
& midp(F,D,E)
& coll(E,A,B)
& eqangle(E,C,C,A,A,C,C,D)
& coll(D,A,B)
& cong(A,C,B,C)
& perp(C,A,C,B) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cong(sk23,sk26,sk23,sk27)
& circle(sk25,sk24,sk27,sk31)
& coll(sk27,sk22,sk23)
& circle(sk25,sk24,sk26,sk30)
& coll(sk26,sk22,sk24)
& circle(sk25,sk24,sk28,sk29)
& midp(sk25,sk23,sk24)
& coll(sk24,sk20,sk21)
& eqangle(sk24,sk22,sk22,sk20,sk20,sk22,sk22,sk23)
& coll(sk23,sk20,sk21)
& cong(sk20,sk22,sk21,sk22)
& perp(sk22,sk20,sk22,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30,sk31])],[f94_nnf]) ).
cnf(c124,plain,
~ cong(sk23,sk26,sk23,sk27),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(t21,plain,
cong(sk23,sk26,sk23,sk27) = false,
inference(equality_encoding,[status(esa)],[c124]) ).
cnf(t3432,plain,
cong(sk23,sk26,sk23,sk27) = false,
inference(orient,[status(thm)],[t21]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD68) ).
fof(f68_nnf,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(t61,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t335,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t61]) ).
cnf(t3434,plain,
true = ifeq(midp(sk23,sk26,sk27),true,false,true),
inference(cp,[status(thm)],[t335,t3432]) ).
cnf(t5824,plain,
ifeq(midp(sk23,sk26,sk27),true,false,true) = true,
inference(orient,[status(thm)],[t3434]) ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD64) ).
fof(f64_nnf,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [M,A,B,C,D] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c64,plain,
( midp(X4,X2,X3)
| ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(t204,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t333,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t204]) ).
fof(f8,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD9) ).
fof(f8_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t141,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t285,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t141]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD8) ).
fof(f7_nnf,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t72,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t292,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t72]) ).
fof(f56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD56) ).
fof(f56_nnf,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [A,P,B,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( perp(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t128,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(t266,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(orient,[status(thm)],[t128]) ).
fof(f73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD73) ).
fof(f73_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t184,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t305,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t184]) ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD20) ).
fof(f19_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t134,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t306,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t134]) ).
fof(f63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD63) ).
fof(f63_nnf,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [M,A,B,C,D] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c63,plain,
( para(X0,X2,X1,X3)
| ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(hi63,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X0,X3,X4),true,para(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(c118,plain,
midp(sk25,sk23,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
midp(sk25,sk23,sk24) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h25,plain,
para(sk23,sk23,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi63,hi118,hi118]) ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD40) ).
fof(f39_nnf,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi39,axiom,
ifeq(para(X0,X1,X2,X3),true,eqangle(X0,X1,X4,X5,X2,X3,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(h143,plain,
eqangle(sk23,sk23,V0,V1,sk24,sk24,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h25]) ).
fof(f20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD21) ).
fof(f20_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi20,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X0,X1,X4,X5,X2,X3,X6,X7),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t26,plain,
eqangle(sk23,sk23,sk24,sk24,X1,X2,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi20,h143]) ).
cnf(t2024,plain,
eqangle(sk23,sk23,sk24,sk24,X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(t2029,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,sk23,sk23,sk24,sk24),true),
inference(cp,[status(thm)],[t306,t2024]) ).
cnf(t22,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t22]) ).
cnf(t23738,plain,
true = eqangle(X1,X2,X1,X2,sk23,sk23,sk24,sk24),
inference(step,[status(thm)],[t2029,t256]) ).
cnf(t8016,plain,
eqangle(X1,X2,X1,X2,sk23,sk23,sk24,sk24) = true,
inference(orient,[status(thm)],[t23738]) ).
cnf(t8021,plain,
true = ifeq(true,true,ifeq(para(sk23,sk23,sk24,sk24),true,para(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t305,t8016]) ).
cnf(t23739,plain,
true = ifeq(para(sk23,sk23,sk24,sk24),true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t8021,t256]) ).
fof(f38,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD39) ).
fof(f38_nnf,plain,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A,B,P,Q,C,D] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( para(X0,X1,X2,X3)
| ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t99,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t314,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t99]) ).
cnf(t25,plain,
eqangle(sk23,sk23,X1,X2,sk24,sk24,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi39,h25]) ).
cnf(t2012,plain,
eqangle(sk23,sk23,X1,X2,sk24,sk24,X1,X2) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(t2014,plain,
true = ifeq(true,true,para(sk23,sk23,sk24,sk24),true),
inference(cp,[status(thm)],[t314,t2012]) ).
cnf(t23576,plain,
true = para(sk23,sk23,sk24,sk24),
inference(step,[status(thm)],[t2014,t256]) ).
cnf(t4662,plain,
para(sk23,sk23,sk24,sk24) = true,
inference(orient,[status(thm)],[t23576]) ).
cnf(t23740,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t23739,t4662]) ).
cnf(t23741,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t23740,t256]) ).
cnf(t8026,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t23741]) ).
cnf(t8043,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),true),
inference(cp,[status(thm)],[t333,t8026]) ).
cnf(t24698,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t8043,t256]) ).
cnf(t24699,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t24698,t8026]) ).
cnf(t24700,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t24699,t256]) ).
cnf(t16742,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t24700]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD67) ).
fof(f67_nnf,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(t119,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t269,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(orient,[status(thm)],[t119]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD3) ).
fof(f2_nnf,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t104,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t278,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(orient,[status(thm)],[t104]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD1) ).
fof(f0_nnf,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t57,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t281,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t57]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD2) ).
fof(f1_nnf,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t58,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t279,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t58]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD66) ).
fof(f66_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(t62,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t353,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t62]) ).
cnf(t8027,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t353,t8026]) ).
cnf(t23742,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t8027,t256]) ).
cnf(t8052,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t23742]) ).
cnf(t8054,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t279,t8052]) ).
cnf(t23743,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t8054,t256]) ).
cnf(t8095,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t23743]) ).
cnf(t8098,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t281,t8095]) ).
cnf(t23744,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t8098,t256]) ).
cnf(t8127,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t23744]) ).
cnf(t8133,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t278,t8127]) ).
cnf(t23745,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t8133,t256]) ).
cnf(t23746,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t23745,t8127]) ).
cnf(t23747,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t23746,t256]) ).
cnf(t8161,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t23747]) ).
cnf(t23758,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t269,t8161]) ).
cnf(t23759,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t23758,t256]) ).
cnf(t8168,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t23759]) ).
cnf(t18220,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t8168]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD23) ).
fof(f22_nnf,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t64,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t263,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t64]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD24) ).
fof(f23_nnf,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t65,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t261,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t65]) ).
fof(f75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( cong(P,Q,U,V)
& eqratio(A,B,C,D,P,Q,U,V) )
=> cong(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD75) ).
fof(f75_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( cong(A,B,C,D)
| ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f75]) ).
fof(f75_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( cong(A,B,C,D)
| ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f75_nnf]) ).
cnf(c75,plain,
( cong(X0,X1,X2,X3)
| ~ cong(X4,X5,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f75_sk]) ).
cnf(t186,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(cong(X5,X6,X7,X8),true,cong(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c75]) ).
cnf(t376,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(cong(X5,X6,X7,X8),true,cong(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t186]) ).
fof(f25,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(B,A,C,D,P,Q,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD26) ).
fof(f25_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(B,A,C,D,P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(B,A,C,D,P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
( eqratio(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(t136,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X2,X1,X3,X4,X5,X6,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t384,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X2,X1,X3,X4,X5,X6,X7,X8),true) = true,
inference(orient,[status(thm)],[t136]) ).
fof(f28,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD29) ).
fof(f28_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,P,Q,C,D,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,P,Q,C,D,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( eqratio(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t135,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t386,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(orient,[status(thm)],[t135]) ).
fof(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD69) ).
fof(f69_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f69]) ).
fof(f69_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f69_nnf]) ).
cnf(c69,plain,
( coll(X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f69_sk]) ).
cnf(hi69,axiom,
ifeq(midp(X0,X1,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c69]) ).
cnf(h23,plain,
coll(sk25,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi69,hi118]) ).
cnf(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h88,plain,
coll(sk23,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi1,h23]) ).
cnf(hi2,axiom,
ifeq(coll(X0,X1,X2),true,ifeq(coll(X0,X1,X3),true,coll(X2,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h363,plain,
coll(sk24,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h88,h88]) ).
cnf(c120,plain,
coll(sk26,sk22,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi120,negated_conjecture,
coll(sk26,sk22,sk24) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(h29,plain,
coll(sk24,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi120,hi120]) ).
cnf(h1838,plain,
coll(sk26,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h29,h363]) ).
fof(f65,axiom,
! [A,B,C,D,O] :
( ( coll(O,B,D)
& coll(O,A,C)
& para(A,B,C,D) )
=> eqratio(O,A,A,C,O,B,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD65) ).
fof(f65_nnf,plain,
! [A,B,C,D,O] :
( eqratio(O,A,A,C,O,B,B,D)
| ~ coll(O,B,D)
| ~ coll(O,A,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [A,B,C,D,O] :
( eqratio(O,A,A,C,O,B,B,D)
| ~ coll(O,B,D)
| ~ coll(O,A,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c65,plain,
( eqratio(X4,X0,X0,X2,X4,X1,X1,X3)
| ~ coll(X4,X1,X3)
| ~ coll(X4,X0,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(hi65,axiom,
ifeq(para(X0,X1,X2,X3),true,ifeq(coll(X4,X0,X2),true,ifeq(coll(X4,X1,X3),true,eqratio(X4,X0,X0,X2,X4,X1,X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(t37,plain,
eqratio(sk26,sk23,sk23,sk24,sk26,sk23,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi65,h25,h1838,h1838]) ).
cnf(t3362,plain,
eqratio(sk26,sk23,sk23,sk24,sk26,sk23,sk23,sk24) = true,
inference(orient,[status(thm)],[t37]) ).
cnf(t3363,plain,
true = ifeq(true,true,eqratio(sk26,sk23,sk26,sk23,sk23,sk24,sk23,sk24),true),
inference(cp,[status(thm)],[t386,t3362]) ).
cnf(t23841,plain,
true = eqratio(sk26,sk23,sk26,sk23,sk23,sk24,sk23,sk24),
inference(step,[status(thm)],[t3363,t256]) ).
cnf(t8472,plain,
eqratio(sk26,sk23,sk26,sk23,sk23,sk24,sk23,sk24) = true,
inference(orient,[status(thm)],[t23841]) ).
cnf(t8474,plain,
true = ifeq(true,true,eqratio(sk23,sk26,sk26,sk23,sk23,sk24,sk23,sk24),true),
inference(cp,[status(thm)],[t384,t8472]) ).
cnf(t23950,plain,
true = eqratio(sk23,sk26,sk26,sk23,sk23,sk24,sk23,sk24),
inference(step,[status(thm)],[t8474,t256]) ).
cnf(t9627,plain,
eqratio(sk23,sk26,sk26,sk23,sk23,sk24,sk23,sk24) = true,
inference(orient,[status(thm)],[t23950]) ).
cnf(t9635,plain,
true = ifeq(true,true,ifeq(cong(sk23,sk24,sk23,sk24),true,cong(sk23,sk26,sk26,sk23),true),true),
inference(cp,[status(thm)],[t376,t9627]) ).
cnf(t23951,plain,
true = ifeq(cong(sk23,sk24,sk23,sk24),true,cong(sk23,sk26,sk26,sk23),true),
inference(step,[status(thm)],[t9635,t256]) ).
fof(f27,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD28) ).
fof(f27_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(P,Q,U,V,A,B,C,D)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(P,Q,U,V,A,B,C,D)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( eqratio(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(t138,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t380,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t138]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD11) ).
fof(f10_nnf,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [M,B,A] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(midp(X0,X1,X2),true,midp(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h27,plain,
midp(sk25,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi118]) ).
fof(f70,axiom,
! [A,B,C,D,M,N] :
( ( midp(N,C,D)
& midp(M,A,B) )
=> eqratio(M,A,A,B,N,C,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD70) ).
fof(f70_nnf,plain,
! [A,B,C,D,M,N] :
( eqratio(M,A,A,B,N,C,C,D)
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f70]) ).
fof(f70_sk,plain,
! [M,A,B,N,C,D] :
( eqratio(M,A,A,B,N,C,C,D)
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f70_nnf]) ).
cnf(c70,plain,
( eqratio(X4,X0,X0,X1,X5,X2,X2,X3)
| ~ midp(X5,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
cnf(hi70,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X3,X4,X5),true,eqratio(X0,X1,X1,X2,X3,X4,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c70]) ).
cnf(t35,plain,
eqratio(sk25,sk24,sk24,sk23,sk25,sk23,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi70,h27,hi118]) ).
cnf(t3289,plain,
eqratio(sk25,sk24,sk24,sk23,sk25,sk23,sk23,sk24) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t3290,plain,
true = ifeq(true,true,eqratio(sk25,sk24,sk25,sk23,sk24,sk23,sk23,sk24),true),
inference(cp,[status(thm)],[t386,t3289]) ).
cnf(t23825,plain,
true = eqratio(sk25,sk24,sk25,sk23,sk24,sk23,sk23,sk24),
inference(step,[status(thm)],[t3290,t256]) ).
cnf(t8318,plain,
eqratio(sk25,sk24,sk25,sk23,sk24,sk23,sk23,sk24) = true,
inference(orient,[status(thm)],[t23825]) ).
cnf(t8323,plain,
true = ifeq(true,true,eqratio(sk24,sk23,sk23,sk24,sk25,sk24,sk25,sk23),true),
inference(cp,[status(thm)],[t380,t8318]) ).
cnf(t23908,plain,
true = eqratio(sk24,sk23,sk23,sk24,sk25,sk24,sk25,sk23),
inference(step,[status(thm)],[t8323,t256]) ).
cnf(t9181,plain,
eqratio(sk24,sk23,sk23,sk24,sk25,sk24,sk25,sk23) = true,
inference(orient,[status(thm)],[t23908]) ).
cnf(t9189,plain,
true = ifeq(true,true,ifeq(cong(sk25,sk24,sk25,sk23),true,cong(sk24,sk23,sk23,sk24),true),true),
inference(cp,[status(thm)],[t376,t9181]) ).
cnf(t23909,plain,
true = ifeq(cong(sk25,sk24,sk25,sk23),true,cong(sk24,sk23,sk23,sk24),true),
inference(step,[status(thm)],[t9189,t256]) ).
cnf(t16,plain,
midp(sk25,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi118]) ).
cnf(t2068,plain,
midp(sk25,sk24,sk23) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t2072,plain,
true = ifeq(true,true,cong(sk25,sk24,sk25,sk23),true),
inference(cp,[status(thm)],[t335,t2068]) ).
cnf(t23577,plain,
true = cong(sk25,sk24,sk25,sk23),
inference(step,[status(thm)],[t2072,t256]) ).
cnf(t4685,plain,
cong(sk25,sk24,sk25,sk23) = true,
inference(orient,[status(thm)],[t23577]) ).
cnf(t23910,plain,
true = ifeq(true,true,cong(sk24,sk23,sk23,sk24),true),
inference(step,[status(thm)],[t23909,t4685]) ).
cnf(t23911,plain,
true = cong(sk24,sk23,sk23,sk24),
inference(step,[status(thm)],[t23910,t256]) ).
cnf(t9190,plain,
cong(sk24,sk23,sk23,sk24) = true,
inference(orient,[status(thm)],[t23911]) ).
cnf(t9193,plain,
true = ifeq(true,true,cong(sk23,sk24,sk24,sk23),true),
inference(cp,[status(thm)],[t261,t9190]) ).
cnf(t23913,plain,
true = cong(sk23,sk24,sk24,sk23),
inference(step,[status(thm)],[t9193,t256]) ).
cnf(t9229,plain,
cong(sk23,sk24,sk24,sk23) = true,
inference(orient,[status(thm)],[t23913]) ).
cnf(t9231,plain,
true = ifeq(true,true,cong(sk23,sk24,sk23,sk24),true),
inference(cp,[status(thm)],[t263,t9229]) ).
cnf(t23914,plain,
true = cong(sk23,sk24,sk23,sk24),
inference(step,[status(thm)],[t9231,t256]) ).
cnf(t9238,plain,
cong(sk23,sk24,sk23,sk24) = true,
inference(orient,[status(thm)],[t23914]) ).
cnf(t23952,plain,
true = ifeq(true,true,cong(sk23,sk26,sk26,sk23),true),
inference(step,[status(thm)],[t23951,t9238]) ).
cnf(t23953,plain,
true = cong(sk23,sk26,sk26,sk23),
inference(step,[status(thm)],[t23952,t256]) ).
cnf(t9636,plain,
cong(sk23,sk26,sk26,sk23) = true,
inference(orient,[status(thm)],[t23953]) ).
cnf(t9639,plain,
true = ifeq(true,true,cong(sk26,sk23,sk23,sk26),true),
inference(cp,[status(thm)],[t261,t9636]) ).
cnf(t23955,plain,
true = cong(sk26,sk23,sk23,sk26),
inference(step,[status(thm)],[t9639,t256]) ).
cnf(t9675,plain,
cong(sk26,sk23,sk23,sk26) = true,
inference(orient,[status(thm)],[t23955]) ).
cnf(t9677,plain,
true = ifeq(true,true,cong(sk26,sk23,sk26,sk23),true),
inference(cp,[status(thm)],[t263,t9675]) ).
cnf(t23956,plain,
true = cong(sk26,sk23,sk26,sk23),
inference(step,[status(thm)],[t9677,t256]) ).
cnf(t9684,plain,
cong(sk26,sk23,sk26,sk23) = true,
inference(orient,[status(thm)],[t23956]) ).
cnf(t18221,plain,
true = ifeq(true,true,midp(sk26,sk23,sk23),true),
inference(cp,[status(thm)],[t18220,t9684]) ).
cnf(t24893,plain,
true = midp(sk26,sk23,sk23),
inference(step,[status(thm)],[t18221,t256]) ).
cnf(t18260,plain,
midp(sk26,sk23,sk23) = true,
inference(orient,[status(thm)],[t24893]) ).
cnf(t18263,plain,
true = ifeq(true,true,midp(sk26,X1,X1),true),
inference(cp,[status(thm)],[t16742,t18260]) ).
cnf(t24906,plain,
true = midp(sk26,X1,X1),
inference(step,[status(thm)],[t18263,t256]) ).
cnf(t18544,plain,
midp(sk26,X1,X1) = true,
inference(orient,[status(thm)],[t24906]) ).
cnf(t18549,plain,
true = ifeq(true,true,cong(sk26,X1,sk26,X1),true),
inference(cp,[status(thm)],[t335,t18544]) ).
cnf(t24917,plain,
true = cong(sk26,X1,sk26,X1),
inference(step,[status(thm)],[t18549,t256]) ).
cnf(t18760,plain,
cong(sk26,X1,sk26,X1) = true,
inference(orient,[status(thm)],[t24917]) ).
cnf(t18774,plain,
true = ifeq(true,true,ifeq(cong(sk26,X1,sk26,X1),true,perp(sk26,sk26,X2,X1),true),true),
inference(cp,[status(thm)],[t266,t18760]) ).
cnf(t24948,plain,
true = ifeq(cong(sk26,X1,sk26,X1),true,perp(sk26,sk26,X2,X1),true),
inference(step,[status(thm)],[t18774,t256]) ).
cnf(t24949,plain,
true = ifeq(true,true,perp(sk26,sk26,X2,X1),true),
inference(step,[status(thm)],[t24948,t18760]) ).
cnf(t24950,plain,
true = perp(sk26,sk26,X2,X1),
inference(step,[status(thm)],[t24949,t256]) ).
cnf(t19300,plain,
perp(sk26,sk26,X1,X2) = true,
inference(orient,[status(thm)],[t24950]) ).
cnf(t19301,plain,
true = ifeq(true,true,perp(X1,X2,sk26,sk26),true),
inference(cp,[status(thm)],[t292,t19300]) ).
cnf(t25003,plain,
true = perp(X1,X2,sk26,sk26),
inference(step,[status(thm)],[t19301,t256]) ).
cnf(t19956,plain,
perp(X1,X2,sk26,sk26) = true,
inference(orient,[status(thm)],[t25003]) ).
cnf(t19963,plain,
true = ifeq(true,true,ifeq(perp(sk26,sk26,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t19956]) ).
cnf(t25021,plain,
true = ifeq(perp(sk26,sk26,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t19963,t256]) ).
cnf(t25022,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t25021,t19300]) ).
cnf(t25023,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t25022,t256]) ).
cnf(t20510,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t25023]) ).
cnf(t25035,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(step,[status(thm)],[t333,t20510]) ).
cnf(t25036,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t25035,t256]) ).
cnf(t25037,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t25036,t20510]) ).
cnf(t25038,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t25037,t256]) ).
cnf(t20517,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t25038]) ).
cnf(t23468,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t20517]) ).
cnf(t18763,plain,
true = ifeq(true,true,cong(sk26,X1,X1,sk26),true),
inference(cp,[status(thm)],[t263,t18760]) ).
cnf(t24947,plain,
true = cong(sk26,X1,X1,sk26),
inference(step,[status(thm)],[t18763,t256]) ).
cnf(t19270,plain,
cong(sk26,X1,X1,sk26) = true,
inference(orient,[status(thm)],[t24947]) ).
cnf(t19272,plain,
true = ifeq(true,true,cong(X1,sk26,sk26,X1),true),
inference(cp,[status(thm)],[t261,t19270]) ).
cnf(t25002,plain,
true = cong(X1,sk26,sk26,X1),
inference(step,[status(thm)],[t19272,t256]) ).
cnf(t19930,plain,
cong(X1,sk26,sk26,X1) = true,
inference(orient,[status(thm)],[t25002]) ).
cnf(t19932,plain,
true = ifeq(true,true,cong(X1,sk26,X1,sk26),true),
inference(cp,[status(thm)],[t263,t19930]) ).
cnf(t25018,plain,
true = cong(X1,sk26,X1,sk26),
inference(step,[status(thm)],[t19932,t256]) ).
cnf(t20436,plain,
cong(X1,sk26,X1,sk26) = true,
inference(orient,[status(thm)],[t25018]) ).
cnf(t20437,plain,
true = ifeq(true,true,midp(X1,sk26,sk26),true),
inference(cp,[status(thm)],[t18220,t20436]) ).
cnf(t25019,plain,
true = midp(X1,sk26,sk26),
inference(step,[status(thm)],[t20437,t256]) ).
cnf(t20466,plain,
midp(X1,sk26,sk26) = true,
inference(orient,[status(thm)],[t25019]) ).
cnf(t20467,plain,
true = ifeq(true,true,midp(X1,X2,X2),true),
inference(cp,[status(thm)],[t16742,t20466]) ).
cnf(t25020,plain,
true = midp(X1,X2,X2),
inference(step,[status(thm)],[t20467,t256]) ).
cnf(t20485,plain,
midp(X1,X2,X2) = true,
inference(orient,[status(thm)],[t25020]) ).
cnf(t23469,plain,
true = ifeq(true,true,midp(X1,X2,X3),true),
inference(cp,[status(thm)],[t23468,t20485]) ).
cnf(t25345,plain,
true = midp(X1,X2,X3),
inference(step,[status(thm)],[t23469,t256]) ).
cnf(t23510,plain,
midp(X1,X2,X3) = true,
inference(orient,[status(thm)],[t25345]) ).
cnf(t25346,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t5824,t23510]) ).
cnf(t25347,plain,
false = true,
inference(step,[status(thm)],[t25346,t256]) ).
cnf(t23511,plain,
false = true,
inference(rw,[status(thm)],[t25347]) ).
cnf(t23527,plain,
false = true,
inference(orient,[status(thm)],[t23511]) ).
cnf(t25364,plain,
cong(sk23,sk26,sk23,sk27) = true,
inference(step,[status(thm)],[t3432,t23527]) ).
cnf(t23528,plain,
cong(sk23,sk26,sk23,sk27) = true,
inference(orient,[status(thm)],[t25364]) ).
cnf(goal_0,negated_conjecture,
cong(sk23,sk26,sk23,sk27) != true,
inference(equality_encoding,[status(esa)],[c124]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t23528]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO619+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n018.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 : Wed Sep 23 12:36:33 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 136.86/20.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 136.86/20.22 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------