%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO598+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 01:18:15 PM UTC 2026
% Result : Theorem 122.58s 22.20s
% Output : Proof 122.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 68
% Number of leaves : 22
% Syntax : Number of formulae : 226 ( 142 unt; 0 def)
% Number of atoms : 392 ( 138 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 268 ( 102 ~; 96 |; 48 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-6 aty)
% Number of variables : 852 ( 108 sgn 344 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD22) ).
fof(f21_nnf,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t240,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(eqangle(X5,X6,X7,X8,X9,X10,X11,X12),true,eqangle(X1,X2,X3,X4,X9,X10,X11,X12),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t304,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(eqangle(X5,X6,X7,X8,X9,X10,X11,X12),true,eqangle(X1,X2,X3,X4,X9,X10,X11,X12),true),true) = true,
inference(orient,[status(thm)],[t240]) ).
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/sandbox/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(t171,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)],[t171]) ).
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/sandbox/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(t168,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)],[t168]) ).
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/sandbox/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(t137,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)],[t137]) ).
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/sandbox/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(t178,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)],[t178]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/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(t88,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)],[t88]) ).
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/sandbox/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(t165,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)],[t165]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/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(t78,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)],[t78]) ).
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/sandbox/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(t218,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)],[t218]) ).
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/sandbox/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(t136,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)],[t136]) ).
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/sandbox/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(t170,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)],[t170]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD41) ).
fof(f40_nnf,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(t135,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t359,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t135]) ).
fof(f81,axiom,
! [A,B,C,D,M,N] :
? [P] :
( ( midp(N,C,D)
& midp(M,A,B) )
=> ( para(P,N,A,C)
& para(P,M,B,D)
& midp(P,A,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleX6) ).
fof(f81_nnf,plain,
! [A,B,C,D,M,N] :
? [P] :
( ( para(P,N,A,C)
& para(P,M,B,D)
& midp(P,A,D) )
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f81]) ).
fof(f81_sk,plain,
! [M,A,B,N,C,D] :
( ( para(sk5(A,B,C,D,M,N),N,A,C)
& para(sk5(A,B,C,D,M,N),M,B,D)
& midp(sk5(A,B,C,D,M,N),A,D) )
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f81_nnf]) ).
cnf(c86,plain,
( midp(sk5(X0,X1,X2,X3,X4,X5),X0,X3)
| ~ midp(X5,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f81_sk]) ).
cnf(hi86,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X3,X4,X5),true,midp(sk5(X1,X2,X4,X5,X0,X3),X1,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c86]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G,H,I,NWPNT1] :
( ( coll(I,A,C)
& perp(I,H,A,C)
& circle(D,A,H,NWPNT1)
& coll(H,D,G)
& midp(G,B,A)
& midp(F,A,C)
& midp(E,C,B)
& circle(D,A,B,C) )
=> eqangle(F,G,G,I,I,G,G,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416060) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,I,NWPNT1] :
( ( coll(I,A,C)
& perp(I,H,A,C)
& circle(D,A,H,NWPNT1)
& coll(H,D,G)
& midp(G,B,A)
& midp(F,A,C)
& midp(E,C,B)
& circle(D,A,B,C) )
=> eqangle(F,G,G,I,I,G,G,E) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,H,I,NWPNT1] :
( ~ eqangle(F,G,G,I,I,G,G,E)
& coll(I,A,C)
& perp(I,H,A,C)
& circle(D,A,H,NWPNT1)
& coll(H,D,G)
& midp(G,B,A)
& midp(F,A,C)
& midp(E,C,B)
& circle(D,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ eqangle(sk25,sk26,sk26,sk28,sk28,sk26,sk26,sk24)
& coll(sk28,sk20,sk22)
& perp(sk28,sk27,sk20,sk22)
& circle(sk23,sk20,sk27,sk29)
& coll(sk27,sk23,sk26)
& midp(sk26,sk21,sk20)
& midp(sk25,sk20,sk22)
& midp(sk24,sk22,sk21)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29])],[f94_nnf]) ).
cnf(c114,plain,
midp(sk24,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
midp(sk24,sk22,sk21) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(c115,plain,
midp(sk25,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
midp(sk25,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h17,plain,
midp(sk5(sk22,sk21,sk20,sk22,sk24,sk25),sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi86,hi114,hi115]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(h350,plain,
cong(sk5(sk22,sk21,sk20,sk22,sk24,sk25),sk22,sk5(sk22,sk21,sk20,sk22,sk24,sk25),sk22) = true,
inference(hyper_resolution,[status(thm)],[hi68,h17]) ).
fof(f12,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD13) ).
fof(f12_nnf,plain,
! [A,B,C,D,O] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [O,A,B,C,D] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( cyclic(X0,X1,X2,X3)
| ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(cong(X0,X1,X0,X3),true,ifeq(cong(X0,X1,X0,X4),true,cyclic(X1,X2,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t32,plain,
cyclic(sk22,sk22,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi12,h350,h350,h350]) ).
cnf(t3074,plain,
cyclic(sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t3075,plain,
true = ifeq(true,true,eqangle(sk22,sk22,sk22,sk22,sk22,sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t359,t3074]) ).
cnf(t33,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t33]) ).
cnf(t18873,plain,
true = eqangle(sk22,sk22,sk22,sk22,sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t3075,t256]) ).
cnf(t5649,plain,
eqangle(sk22,sk22,sk22,sk22,sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t18873]) ).
cnf(t5651,plain,
true = ifeq(true,true,para(sk22,sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t314,t5649]) ).
cnf(t18874,plain,
true = para(sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t5651,t256]) ).
cnf(t5672,plain,
para(sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t18874]) ).
cnf(t5674,plain,
true = ifeq(true,true,eqangle(sk22,sk22,X1,X2,sk22,sk22,X1,X2),true),
inference(cp,[status(thm)],[t346,t5672]) ).
cnf(t19003,plain,
true = eqangle(sk22,sk22,X1,X2,sk22,sk22,X1,X2),
inference(step,[status(thm)],[t5674,t256]) ).
cnf(t7886,plain,
eqangle(sk22,sk22,X1,X2,sk22,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t19003]) ).
cnf(t7890,plain,
true = ifeq(true,true,eqangle(X1,X2,sk22,sk22,X1,X2,sk22,sk22),true),
inference(cp,[status(thm)],[t308,t7886]) ).
cnf(t19154,plain,
true = eqangle(X1,X2,sk22,sk22,X1,X2,sk22,sk22),
inference(step,[status(thm)],[t7890,t256]) ).
cnf(t9617,plain,
eqangle(X1,X2,sk22,sk22,X1,X2,sk22,sk22) = true,
inference(orient,[status(thm)],[t19154]) ).
cnf(t9619,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t9617]) ).
cnf(t19155,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t9619,t256]) ).
cnf(t9641,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t19155]) ).
cnf(t9658,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,t9641]) ).
cnf(t20024,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)],[t9658,t256]) ).
cnf(t20025,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t20024,t9641]) ).
cnf(t20026,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t20025,t256]) ).
cnf(t17630,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t20026]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox/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(t146,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)],[t146]) ).
fof(f43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD43) ).
fof(f43_nnf,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(t253,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t357,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t253]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD15) ).
fof(f14_nnf,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t83,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t362,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t83]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD16) ).
fof(f15_nnf,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t84,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t360,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t84]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/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(h26,plain,
midp(sk25,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi115]) ).
cnf(h212,plain,
cong(sk25,sk22,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi68,h26]) ).
cnf(t30,plain,
cyclic(sk22,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi12,h212,h212,h212]) ).
cnf(t3101,plain,
cyclic(sk22,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(t3102,plain,
true = ifeq(true,true,cyclic(sk20,sk22,sk20,sk20),true),
inference(cp,[status(thm)],[t360,t3101]) ).
cnf(t18825,plain,
true = cyclic(sk20,sk22,sk20,sk20),
inference(step,[status(thm)],[t3102,t256]) ).
cnf(t4775,plain,
cyclic(sk20,sk22,sk20,sk20) = true,
inference(orient,[status(thm)],[t18825]) ).
cnf(t4776,plain,
true = ifeq(true,true,cyclic(sk20,sk20,sk22,sk20),true),
inference(cp,[status(thm)],[t362,t4775]) ).
cnf(t18841,plain,
true = cyclic(sk20,sk20,sk22,sk20),
inference(step,[status(thm)],[t4776,t256]) ).
cnf(t5112,plain,
cyclic(sk20,sk20,sk22,sk20) = true,
inference(orient,[status(thm)],[t18841]) ).
cnf(t5115,plain,
true = ifeq(true,true,eqangle(sk22,sk20,sk22,sk20,sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t359,t5112]) ).
cnf(t18982,plain,
true = eqangle(sk22,sk20,sk22,sk20,sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t5115,t256]) ).
cnf(t7689,plain,
eqangle(sk22,sk20,sk22,sk20,sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t18982]) ).
cnf(t7702,plain,
true = ifeq(cyclic(sk20,sk20,sk22,sk20),true,ifeq(cyclic(sk20,sk20,sk22,sk20),true,ifeq(cyclic(sk20,sk20,sk22,sk20),true,ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),true),true),true),
inference(cp,[status(thm)],[t357,t7689]) ).
cnf(t18983,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk20,sk22,sk20),true,ifeq(cyclic(sk20,sk20,sk22,sk20),true,ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),true),true),true),
inference(step,[status(thm)],[t7702,t5112]) ).
cnf(t18984,plain,
true = ifeq(cyclic(sk20,sk20,sk22,sk20),true,ifeq(cyclic(sk20,sk20,sk22,sk20),true,ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),true),true),
inference(step,[status(thm)],[t18983,t256]) ).
cnf(t18985,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk20,sk22,sk20),true,ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),true),true),
inference(step,[status(thm)],[t18984,t5112]) ).
cnf(t18986,plain,
true = ifeq(cyclic(sk20,sk20,sk22,sk20),true,ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),true),
inference(step,[status(thm)],[t18985,t256]) ).
cnf(t18987,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),true),
inference(step,[status(thm)],[t18986,t5112]) ).
cnf(t18988,plain,
true = ifeq(true,true,cong(sk20,sk20,sk20,sk20),true),
inference(step,[status(thm)],[t18987,t256]) ).
cnf(t18989,plain,
true = cong(sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t18988,t256]) ).
cnf(t7703,plain,
cong(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t18989]) ).
cnf(t7713,plain,
true = ifeq(true,true,ifeq(coll(sk20,sk20,sk20),true,midp(sk20,sk20,sk20),true),true),
inference(cp,[status(thm)],[t272,t7703]) ).
cnf(t18990,plain,
true = ifeq(coll(sk20,sk20,sk20),true,midp(sk20,sk20,sk20),true),
inference(step,[status(thm)],[t7713,t256]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/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(t79,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)],[t79]) ).
cnf(t4778,plain,
true = ifeq(true,true,eqangle(sk20,sk20,sk20,sk22,sk20,sk20,sk20,sk22),true),
inference(cp,[status(thm)],[t359,t4775]) ).
cnf(t18971,plain,
true = eqangle(sk20,sk20,sk20,sk22,sk20,sk20,sk20,sk22),
inference(step,[status(thm)],[t4778,t256]) ).
cnf(t7527,plain,
eqangle(sk20,sk20,sk20,sk22,sk20,sk20,sk20,sk22) = true,
inference(orient,[status(thm)],[t18971]) ).
cnf(t7529,plain,
true = ifeq(true,true,para(sk20,sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t314,t7527]) ).
cnf(t18972,plain,
true = para(sk20,sk20,sk20,sk20),
inference(step,[status(thm)],[t7529,t256]) ).
cnf(t7541,plain,
para(sk20,sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t18972]) ).
cnf(t7542,plain,
true = ifeq(true,true,coll(sk20,sk20,sk20),true),
inference(cp,[status(thm)],[t353,t7541]) ).
cnf(t18973,plain,
true = coll(sk20,sk20,sk20),
inference(step,[status(thm)],[t7542,t256]) ).
cnf(t7561,plain,
coll(sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t18973]) ).
cnf(t18991,plain,
true = ifeq(true,true,midp(sk20,sk20,sk20),true),
inference(step,[status(thm)],[t18990,t7561]) ).
cnf(t18992,plain,
true = midp(sk20,sk20,sk20),
inference(step,[status(thm)],[t18991,t256]) ).
cnf(t7741,plain,
midp(sk20,sk20,sk20) = true,
inference(orient,[status(thm)],[t18992]) ).
cnf(t17631,plain,
true = ifeq(true,true,midp(sk20,X1,X1),true),
inference(cp,[status(thm)],[t17630,t7741]) ).
cnf(t20027,plain,
true = midp(sk20,X1,X1),
inference(step,[status(thm)],[t17631,t256]) ).
cnf(t17637,plain,
midp(sk20,X1,X1) = true,
inference(orient,[status(thm)],[t20027]) ).
cnf(t17638,plain,
true = ifeq(true,true,cong(sk20,X1,sk20,X1),true),
inference(cp,[status(thm)],[t336,t17637]) ).
cnf(t20030,plain,
true = cong(sk20,X1,sk20,X1),
inference(step,[status(thm)],[t17638,t256]) ).
cnf(t17697,plain,
cong(sk20,X1,sk20,X1) = true,
inference(orient,[status(thm)],[t20030]) ).
cnf(t17708,plain,
true = ifeq(true,true,ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t17697]) ).
cnf(t20034,plain,
true = ifeq(cong(sk20,X1,sk20,X1),true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t17708,t256]) ).
cnf(t20035,plain,
true = ifeq(true,true,perp(sk20,sk20,X2,X1),true),
inference(step,[status(thm)],[t20034,t17697]) ).
cnf(t20036,plain,
true = perp(sk20,sk20,X2,X1),
inference(step,[status(thm)],[t20035,t256]) ).
cnf(t17823,plain,
perp(sk20,sk20,X1,X2) = true,
inference(orient,[status(thm)],[t20036]) ).
cnf(t17824,plain,
true = ifeq(true,true,perp(X1,X2,sk20,sk20),true),
inference(cp,[status(thm)],[t292,t17823]) ).
cnf(t20046,plain,
true = perp(X1,X2,sk20,sk20),
inference(step,[status(thm)],[t17824,t256]) ).
cnf(t17978,plain,
perp(X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t20046]) ).
cnf(t17985,plain,
true = ifeq(true,true,ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t17978]) ).
cnf(t20052,plain,
true = ifeq(perp(sk20,sk20,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t17985,t256]) ).
cnf(t20053,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t20052,t17823]) ).
cnf(t20054,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t20053,t256]) ).
cnf(t18131,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t20054]) ).
cnf(t20055,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t346,t18131]) ).
cnf(t20056,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t20055,t256]) ).
cnf(t18132,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t20056]) ).
cnf(t18494,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t18132]) ).
cnf(t18496,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true),
inference(cp,[status(thm)],[t312,t18494]) ).
cnf(t20115,plain,
true = eqangle(X1,X2,X3,X4,X5,X6,X5,X6),
inference(step,[status(thm)],[t18496,t256]) ).
cnf(t18576,plain,
eqangle(X1,X2,X3,X4,X5,X6,X5,X6) = true,
inference(orient,[status(thm)],[t20115]) ).
cnf(t18578,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,X3,X4,X5,X6),true),
inference(cp,[status(thm)],[t306,t18576]) ).
cnf(t20129,plain,
true = eqangle(X1,X2,X1,X2,X3,X4,X5,X6),
inference(step,[status(thm)],[t18578,t256]) ).
cnf(t18689,plain,
eqangle(X1,X2,X1,X2,X3,X4,X5,X6) = true,
inference(orient,[status(thm)],[t20129]) ).
cnf(t18696,plain,
true = ifeq(eqangle(X1,X2,X3,X4,X5,X6,X5,X6),true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(cp,[status(thm)],[t304,t18689]) ).
cnf(t20141,plain,
true = ifeq(true,true,ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),true),
inference(step,[status(thm)],[t18696,t18576]) ).
cnf(t20142,plain,
true = ifeq(true,true,eqangle(X1,X2,X3,X4,X7,X8,X9,X10),true),
inference(step,[status(thm)],[t20141,t256]) ).
cnf(t20143,plain,
true = eqangle(X1,X2,X3,X4,X7,X8,X9,X10),
inference(step,[status(thm)],[t20142,t256]) ).
cnf(t18780,plain,
eqangle(X1,X2,X3,X4,X5,X6,X7,X8) = true,
inference(orient,[status(thm)],[t20143]) ).
cnf(c121,plain,
~ eqangle(sk25,sk26,sk26,sk28,sk28,sk26,sk26,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
eqangle(sk25,sk26,sk26,sk28,sk28,sk26,sk26,sk24) != true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t18780]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO598+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.38 % Computer : n026.cluster.edu
% 0.08/5.38 % Model : x86_64 x86_64
% 0.08/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.38 % Memory : 8046.5625MB
% 0.08/5.38 % OS : Linux 6.8.0-71-generic
% 0.08/5.38 % CPULimit : 300
% 0.08/5.38 % WCLimit : 300
% 0.08/5.38 % DateTime : Wed Sep 23 12:33:29 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.08/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 122.58/22.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 122.58/22.20 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------