%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO607+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 : n012.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 01:18:16 PM UTC 2026
% Result : Theorem 132.64s 17.38s
% Output : Proof 132.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 25
% Syntax : Number of formulae : 265 ( 169 unt; 0 def)
% Number of atoms : 418 ( 163 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 255 ( 102 ~; 96 |; 32 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 934 ( 108 sgn 345 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f74,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( perp(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> perp(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD74) ).
fof(f74_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c74,plain,
( perp(X0,X1,X2,X3)
| ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(t207,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(perp(X5,X6,X7,X8),true,perp(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(t301,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(perp(X5,X6,X7,X8),true,perp(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t207]) ).
fof(f86,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX11) ).
fof(f86_nnf,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f86]) ).
fof(f86_sk,plain,
! [O,A,B,C] :
( perp(sk11(A,B,C,O),A,A,O)
| ~ circle(O,A,B,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f86_nnf]) ).
cnf(c99,plain,
( perp(sk11(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f86_sk]) ).
cnf(hi99,axiom,
ifeq(circle(X0,X1,X2,X3),true,perp(sk11(X1,X2,X3,X0),X1,X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c99]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F] :
( ( circle(F,B,D,C)
& circle(E,A,C,D)
& perp(D,A,D,B)
& midp(C,B,A) )
=> perp(E,D,D,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL618069) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F] :
( ( circle(F,B,D,C)
& circle(E,A,C,D)
& perp(D,A,D,B)
& midp(C,B,A) )
=> perp(E,D,D,F) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F] :
( ~ perp(E,D,D,F)
& circle(F,B,D,C)
& circle(E,A,C,D)
& perp(D,A,D,B)
& midp(C,B,A) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk24,sk23,sk23,sk25)
& circle(sk25,sk21,sk23,sk22)
& circle(sk24,sk20,sk22,sk23)
& perp(sk23,sk20,sk23,sk21)
& midp(sk22,sk21,sk20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25])],[f94_nnf]) ).
cnf(c116,plain,
circle(sk25,sk21,sk23,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
circle(sk25,sk21,sk23,sk22) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h16,plain,
perp(sk11(sk21,sk23,sk22,sk25),sk21,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi116]) ).
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(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h104,plain,
perp(sk21,sk25,sk11(sk21,sk23,sk22,sk25),sk21) = true,
inference(hyper_resolution,[status(thm)],[hi7,h16]) ).
fof(f6,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD7) ).
fof(f6_nnf,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t97,plain,
perp(sk21,sk25,sk21,sk11(sk21,sk23,sk22,sk25)) = true,
inference(hyper_resolution,[status(thm)],[hi6,h104]) ).
cnf(t1130,plain,
perp(sk21,sk25,sk21,sk11(sk21,sk23,sk22,sk25)) = true,
inference(orient,[status(thm)],[t97]) ).
cnf(t1140,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk21,sk25,sk21,sk11(sk21,sk23,sk22,sk25)),true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(cp,[status(thm)],[t301,t1130]) ).
cnf(t50,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t50]) ).
cnf(t48732,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk21,sk25,sk21,sk11(sk21,sk23,sk22,sk25)),true,perp(X1,X2,X3,X4),true),
inference(step,[status(thm)],[t1140,t256]) ).
cnf(t40745,plain,
ifeq(eqangle(X1,X2,X3,X4,sk21,sk25,sk21,sk11(sk21,sk23,sk22,sk25)),true,perp(X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t48732]) ).
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(t176,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)],[t176]) ).
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(t173,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t312,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(orient,[status(thm)],[t173]) ).
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(t153,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t346,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t153]) ).
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(t183,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)],[t183]) ).
cnf(t128,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)],[t128]) ).
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(t170,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(t271,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)],[t170]) ).
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(t118,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t336,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t118]) ).
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(t225,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)],[t225]) ).
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(t152,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)],[t152]) ).
fof(f18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD19) ).
fof(f18_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t175,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t308,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(orient,[status(thm)],[t175]) ).
fof(f85,axiom,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,H,A,C)
& perp(A,H,B,C) )
=> ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX10) ).
fof(f85_nnf,plain,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) )
| ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ),
inference(nnf_transformation,[status(thm)],[f85]) ).
fof(f85_sk,plain,
! [A,H,B,C] :
( ( perp(B,sk10(A,B,C,H),C,A)
& coll(sk10(A,B,C,H),C,A)
& perp(A,sk9(A,B,C,H),C,B)
& coll(sk9(A,B,C,H),C,B) )
| ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10])],[f85_nnf]) ).
cnf(c98,plain,
( perp(X1,sk10(X0,X1,X2,X3),X2,X0)
| ~ perp(X1,X3,X0,X2)
| ~ perp(X0,X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f85_sk]) ).
cnf(hi98,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X1,X0,X3),true,perp(X2,sk10(X0,X2,X3,X1),X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c98]) ).
cnf(c114,plain,
perp(sk23,sk20,sk23,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
perp(sk23,sk20,sk23,sk21) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h9,plain,
perp(sk23,sk10(sk23,sk23,sk21,sk20),sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi98,hi114,hi114]) ).
cnf(h76,plain,
perp(sk21,sk23,sk23,sk10(sk23,sk23,sk21,sk20)) = true,
inference(hyper_resolution,[status(thm)],[hi7,h9]) ).
cnf(hi8,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h1082,plain,
para(sk21,sk23,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi8,h76,h9]) ).
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(t69,plain,
eqangle(sk21,sk23,X1,X2,sk21,sk23,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi39,h1082]) ).
cnf(t1564,plain,
eqangle(sk21,sk23,X1,X2,sk21,sk23,X1,X2) = true,
inference(orient,[status(thm)],[t69]) ).
cnf(t1573,plain,
true = ifeq(true,true,eqangle(X1,X2,sk21,sk23,X1,X2,sk21,sk23),true),
inference(cp,[status(thm)],[t308,t1564]) ).
cnf(t46102,plain,
true = eqangle(X1,X2,sk21,sk23,X1,X2,sk21,sk23),
inference(step,[status(thm)],[t1573,t256]) ).
cnf(t10359,plain,
eqangle(X1,X2,sk21,sk23,X1,X2,sk21,sk23) = true,
inference(orient,[status(thm)],[t46102]) ).
cnf(t10362,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t10359]) ).
cnf(t46103,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t10362,t256]) ).
cnf(t10384,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t46103]) ).
cnf(t10401,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,t10384]) ).
cnf(t47881,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)],[t10401,t256]) ).
cnf(t47882,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t47881,t10384]) ).
cnf(t47883,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t47882,t256]) ).
cnf(t28271,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t47883]) ).
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(t161,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(t272,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)],[t161]) ).
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(t157,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(t260,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(orient,[status(thm)],[t157]) ).
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(t111,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t263,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t111]) ).
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(t112,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t261,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t112]) ).
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(t119,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)],[t119]) ).
cnf(t10385,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t353,t10384]) ).
cnf(t46104,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t10385,t256]) ).
cnf(t10410,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t46104]) ).
cnf(t10412,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t261,t10410]) ).
cnf(t46105,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t10412,t256]) ).
cnf(t10453,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t46105]) ).
cnf(t10456,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t263,t10453]) ).
cnf(t46106,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t10456,t256]) ).
cnf(t10485,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t46106]) ).
cnf(t10488,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t260,t10485]) ).
cnf(t46107,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t10488,t256]) ).
cnf(t46108,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t46107,t10485]) ).
cnf(t46109,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t46108,t256]) ).
cnf(t10519,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t46109]) ).
cnf(t46120,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t272,t10519]) ).
cnf(t46121,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t46120,t256]) ).
cnf(t10526,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t46121]) ).
cnf(t30007,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t10526]) ).
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(t120,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t268,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t120]) ).
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(t121,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t266,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t121]) ).
cnf(c115,plain,
circle(sk24,sk20,sk22,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
circle(sk24,sk20,sk22,sk23) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h15,plain,
perp(sk11(sk20,sk22,sk23,sk24),sk20,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi115]) ).
cnf(h100,plain,
perp(sk20,sk24,sk11(sk20,sk22,sk23,sk24),sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,h15]) ).
cnf(h1293,plain,
para(sk20,sk24,sk20,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi8,h100,h15]) ).
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(c113,plain,
midp(sk22,sk21,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
midp(sk22,sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h4,plain,
coll(sk22,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi69,hi113]) ).
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(h21,plain,
coll(sk20,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h4,h4]) ).
cnf(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h79,plain,
coll(sk20,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h21]) ).
cnf(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h127,plain,
coll(sk22,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi1,h79]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(h5,plain,
cong(sk22,sk21,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi68,hi113]) ).
cnf(hi23,axiom,
ifeq(cong(X0,X1,X2,X3),true,cong(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h45,plain,
cong(sk22,sk20,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi23,h5]) ).
fof(f24,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD25) ).
fof(f24_nnf,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi24,axiom,
ifeq(cong(X0,X1,X2,X3),true,ifeq(cong(X2,X3,X4,X5),true,cong(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h372,plain,
cong(sk22,sk20,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi24,h45,h5]) ).
cnf(hi67,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(coll(X0,X1,X2),true,midp(X0,X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(h6530,plain,
midp(sk22,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi67,h372,h127]) ).
cnf(hi64,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(para(X1,X3,X2,X4),true,ifeq(para(X1,X4,X2,X3),true,midp(X0,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(h13659,plain,
midp(sk22,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi64,h6530,h1293,h1293]) ).
cnf(t35,plain,
cong(sk22,sk24,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi68,h13659]) ).
cnf(t1071,plain,
cong(sk22,sk24,sk22,sk24) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t1075,plain,
true = ifeq(true,true,cong(sk22,sk24,sk24,sk22),true),
inference(cp,[status(thm)],[t268,t1071]) ).
cnf(t45838,plain,
true = cong(sk22,sk24,sk24,sk22),
inference(step,[status(thm)],[t1075,t256]) ).
cnf(t4234,plain,
cong(sk22,sk24,sk24,sk22) = true,
inference(orient,[status(thm)],[t45838]) ).
cnf(t4236,plain,
true = ifeq(true,true,cong(sk24,sk22,sk22,sk24),true),
inference(cp,[status(thm)],[t266,t4234]) ).
cnf(t45863,plain,
true = cong(sk24,sk22,sk22,sk24),
inference(step,[status(thm)],[t4236,t256]) ).
cnf(t4806,plain,
cong(sk24,sk22,sk22,sk24) = true,
inference(orient,[status(thm)],[t45863]) ).
cnf(t4808,plain,
true = ifeq(true,true,cong(sk24,sk22,sk24,sk22),true),
inference(cp,[status(thm)],[t268,t4806]) ).
cnf(t45889,plain,
true = cong(sk24,sk22,sk24,sk22),
inference(step,[status(thm)],[t4808,t256]) ).
cnf(t5493,plain,
cong(sk24,sk22,sk24,sk22) = true,
inference(orient,[status(thm)],[t45889]) ).
cnf(t30010,plain,
true = ifeq(true,true,midp(sk24,sk22,sk22),true),
inference(cp,[status(thm)],[t30007,t5493]) ).
cnf(t48088,plain,
true = midp(sk24,sk22,sk22),
inference(step,[status(thm)],[t30010,t256]) ).
cnf(t30110,plain,
midp(sk24,sk22,sk22) = true,
inference(orient,[status(thm)],[t48088]) ).
cnf(t30111,plain,
true = ifeq(true,true,midp(sk24,X1,X1),true),
inference(cp,[status(thm)],[t28271,t30110]) ).
cnf(t48126,plain,
true = midp(sk24,X1,X1),
inference(step,[status(thm)],[t30111,t256]) ).
cnf(t30791,plain,
midp(sk24,X1,X1) = true,
inference(orient,[status(thm)],[t48126]) ).
cnf(t30800,plain,
true = ifeq(true,true,cong(sk24,X1,sk24,X1),true),
inference(cp,[status(thm)],[t336,t30791]) ).
cnf(t48180,plain,
true = cong(sk24,X1,sk24,X1),
inference(step,[status(thm)],[t30800,t256]) ).
cnf(t31869,plain,
cong(sk24,X1,sk24,X1) = true,
inference(orient,[status(thm)],[t48180]) ).
cnf(t31886,plain,
true = ifeq(true,true,ifeq(cong(sk24,X1,sk24,X1),true,perp(sk24,sk24,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t31869]) ).
cnf(t48273,plain,
true = ifeq(cong(sk24,X1,sk24,X1),true,perp(sk24,sk24,X2,X1),true),
inference(step,[status(thm)],[t31886,t256]) ).
cnf(t48274,plain,
true = ifeq(true,true,perp(sk24,sk24,X2,X1),true),
inference(step,[status(thm)],[t48273,t31869]) ).
cnf(t48275,plain,
true = perp(sk24,sk24,X2,X1),
inference(step,[status(thm)],[t48274,t256]) ).
cnf(t33523,plain,
perp(sk24,sk24,X1,X2) = true,
inference(orient,[status(thm)],[t48275]) ).
cnf(t33524,plain,
true = ifeq(true,true,perp(X1,X2,sk24,sk24),true),
inference(cp,[status(thm)],[t292,t33523]) ).
cnf(t48372,plain,
true = perp(X1,X2,sk24,sk24),
inference(step,[status(thm)],[t33524,t256]) ).
cnf(t34987,plain,
perp(X1,X2,sk24,sk24) = true,
inference(orient,[status(thm)],[t48372]) ).
cnf(t34994,plain,
true = ifeq(true,true,ifeq(perp(sk24,sk24,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t34987]) ).
cnf(t48458,plain,
true = ifeq(perp(sk24,sk24,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t34994,t256]) ).
cnf(t48459,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t48458,t33523]) ).
cnf(t48460,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t48459,t256]) ).
cnf(t36530,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t48460]) ).
cnf(t48461,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t346,t36530]) ).
cnf(t48462,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t48461,t256]) ).
cnf(t36531,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t48462]) ).
cnf(t43880,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t36531]) ).
cnf(t43882,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t312,t43880]) ).
cnf(t49016,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t43882,t256]) ).
cnf(t45232,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t49016]) ).
cnf(t45234,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t306,t45232]) ).
cnf(t49090,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t45234,t256]) ).
cnf(t45736,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t49090]) ).
cnf(t45740,plain,
true = ifeq(true,true,perp(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t40745,t45736]) ).
cnf(t49091,plain,
true = perp(X1,X2,X1,X2),
inference(step,[status(thm)],[t45740,t256]) ).
cnf(t45748,plain,
perp(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t49091]) ).
cnf(t45753,plain,
true = ifeq(eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(cp,[status(thm)],[t301,t45748]) ).
cnf(t49093,plain,
true = ifeq(true,true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(step,[status(thm)],[t45753,t45232]) ).
cnf(t49094,plain,
true = ifeq(true,true,perp(X1,X2,X3,X4),true),
inference(step,[status(thm)],[t49093,t256]) ).
cnf(t49095,plain,
true = perp(X1,X2,X3,X4),
inference(step,[status(thm)],[t49094,t256]) ).
cnf(t45784,plain,
perp(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t49095]) ).
cnf(c117,plain,
~ perp(sk24,sk23,sk23,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
perp(sk24,sk23,sk23,sk25) != true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t45784]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO607+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Wed Sep 23 12:31:51 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 132.64/17.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 132.64/17.38 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------