%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO623+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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:18:19 PM UTC 2026
% Result : Theorem 168.62s 22.28s
% Output : Proof 168.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 16
% Syntax : Number of formulae : 175 ( 115 unt; 0 def)
% Number of atoms : 283 ( 111 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 174 ( 66 ~; 60 |; 32 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-4 aty)
% Number of variables : 572 ( 54 sgn 238 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f94,conjecture,
! [A,B,C,D,E,F,G,H] :
( ( coll(H,D,E)
& coll(H,B,G)
& coll(G,D,F)
& eqangle(G,B,B,C,G,B,B,A)
& midp(F,A,B)
& midp(E,B,C)
& midp(D,C,A) )
=> cong(D,G,D,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL8110986) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H] :
( ( coll(H,D,E)
& coll(H,B,G)
& coll(G,D,F)
& eqangle(G,B,B,C,G,B,B,A)
& midp(F,A,B)
& midp(E,B,C)
& midp(D,C,A) )
=> cong(D,G,D,H) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,H] :
( ~ cong(D,G,D,H)
& coll(H,D,E)
& coll(H,B,G)
& coll(G,D,F)
& eqangle(G,B,B,C,G,B,B,A)
& midp(F,A,B)
& midp(E,B,C)
& midp(D,C,A) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cong(sk23,sk26,sk23,sk27)
& coll(sk27,sk23,sk24)
& coll(sk27,sk21,sk26)
& coll(sk26,sk23,sk25)
& eqangle(sk26,sk21,sk21,sk22,sk26,sk21,sk21,sk20)
& midp(sk25,sk20,sk21)
& midp(sk24,sk21,sk22)
& midp(sk23,sk22,sk20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27])],[f94_nnf]) ).
cnf(c120,plain,
~ cong(sk23,sk26,sk23,sk27),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(t42,plain,
cong(sk23,sk26,sk23,sk27) = false,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(t3414,plain,
cong(sk23,sk26,sk23,sk27) = false,
inference(orient,[status(thm)],[t42]) ).
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(t128,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t316,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t128]) ).
cnf(t3416,plain,
true = ifeq(midp(sk23,sk26,sk27),true,false,true),
inference(cp,[status(thm)],[t316,t3414]) ).
cnf(t5927,plain,
ifeq(midp(sk23,sk26,sk27),true,false,true) = true,
inference(orient,[status(thm)],[t3416]) ).
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(t226,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(t313,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)],[t226]) ).
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(t189,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(t322,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)],[t189]) ).
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(t138,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t327,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t138]) ).
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(t176,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)],[t176]) ).
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(t208,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(t285,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)],[t208]) ).
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(t179,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(t292,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)],[t179]) ).
fof(f44,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD44) ).
fof(f44_nnf,plain,
! [A,B,C,E,F] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [E,A,B,F,C] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
( para(X3,X4,X1,X2)
| ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi44,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X3,X1,X4),true,para(X0,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(c113,plain,
midp(sk23,sk22,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
midp(sk23,sk22,sk20) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h7,plain,
para(sk23,sk23,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi44,hi113,hi113]) ).
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(h155,plain,
eqangle(sk23,sk23,V0,V1,sk20,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h7]) ).
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(hi18,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X2,X3,X0,X1,X6,X7,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t71,plain,
eqangle(X1,X2,sk23,sk23,X1,X2,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi18,h155]) ).
cnf(t1594,plain,
eqangle(X1,X2,sk23,sk23,X1,X2,sk20,sk20) = true,
inference(orient,[status(thm)],[t71]) ).
cnf(t1595,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,sk23,sk23,sk20,sk20),true),
inference(cp,[status(thm)],[t292,t1594]) ).
cnf(t52,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t52]) ).
cnf(t24382,plain,
true = eqangle(X1,X2,X1,X2,sk23,sk23,sk20,sk20),
inference(step,[status(thm)],[t1595,t256]) ).
cnf(t7163,plain,
eqangle(X1,X2,X1,X2,sk23,sk23,sk20,sk20) = true,
inference(orient,[status(thm)],[t24382]) ).
cnf(t7168,plain,
true = ifeq(true,true,ifeq(para(sk23,sk23,sk20,sk20),true,para(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t7163]) ).
cnf(t24383,plain,
true = ifeq(para(sk23,sk23,sk20,sk20),true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t7168,t256]) ).
cnf(t58,plain,
para(sk23,sk23,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi44,hi113,hi113]) ).
cnf(t2647,plain,
para(sk23,sk23,sk20,sk20) = true,
inference(orient,[status(thm)],[t58]) ).
cnf(t24384,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t24383,t2647]) ).
cnf(t24385,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t24384,t256]) ).
cnf(t7173,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t24385]) ).
cnf(t7190,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)],[t313,t7173]) ).
cnf(t26179,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)],[t7190,t256]) ).
cnf(t26180,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t26179,t7173]) ).
cnf(t26181,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t26180,t256]) ).
cnf(t23345,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t26181]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD4) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t135,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t350,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t135]) ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD5) ).
fof(f4_nnf,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t136,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t347,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t136]) ).
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(t160,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(t294,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t160]) ).
cnf(c116,plain,
eqangle(sk26,sk21,sk21,sk22,sk26,sk21,sk21,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
eqangle(sk26,sk21,sk21,sk22,sk26,sk21,sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(t74,plain,
eqangle(sk21,sk22,sk26,sk21,sk21,sk20,sk26,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi116]) ).
cnf(t1718,plain,
eqangle(sk21,sk22,sk26,sk21,sk21,sk20,sk26,sk21) = true,
inference(orient,[status(thm)],[t74]) ).
cnf(t1720,plain,
true = ifeq(true,true,para(sk21,sk22,sk21,sk20),true),
inference(cp,[status(thm)],[t294,t1718]) ).
cnf(t24264,plain,
true = para(sk21,sk22,sk21,sk20),
inference(step,[status(thm)],[t1720,t256]) ).
cnf(t4558,plain,
para(sk21,sk22,sk21,sk20) = true,
inference(orient,[status(thm)],[t24264]) ).
cnf(t4560,plain,
true = ifeq(true,true,para(sk21,sk22,sk20,sk21),true),
inference(cp,[status(thm)],[t350,t4558]) ).
cnf(t24292,plain,
true = para(sk21,sk22,sk20,sk21),
inference(step,[status(thm)],[t4560,t256]) ).
cnf(t5297,plain,
para(sk21,sk22,sk20,sk21) = true,
inference(orient,[status(thm)],[t24292]) ).
cnf(t5298,plain,
true = ifeq(true,true,para(sk20,sk21,sk21,sk22),true),
inference(cp,[status(thm)],[t347,t5297]) ).
cnf(t24306,plain,
true = para(sk20,sk21,sk21,sk22),
inference(step,[status(thm)],[t5298,t256]) ).
cnf(t5567,plain,
para(sk20,sk21,sk21,sk22) = true,
inference(orient,[status(thm)],[t24306]) ).
cnf(t5568,plain,
true = ifeq(true,true,para(sk20,sk21,sk22,sk21),true),
inference(cp,[status(thm)],[t350,t5567]) ).
cnf(t24318,plain,
true = para(sk20,sk21,sk22,sk21),
inference(step,[status(thm)],[t5568,t256]) ).
cnf(t5762,plain,
para(sk20,sk21,sk22,sk21) = true,
inference(orient,[status(thm)],[t24318]) ).
cnf(t5781,plain,
true = ifeq(midp(X1,sk20,sk22),true,ifeq(true,true,ifeq(para(sk20,sk21,sk22,sk21),true,midp(X1,sk21,sk21),true),true),true),
inference(cp,[status(thm)],[t313,t5762]) ).
cnf(t26144,plain,
true = ifeq(midp(X1,sk20,sk22),true,ifeq(para(sk20,sk21,sk22,sk21),true,midp(X1,sk21,sk21),true),true),
inference(step,[status(thm)],[t5781,t256]) ).
cnf(t26145,plain,
true = ifeq(midp(X1,sk20,sk22),true,ifeq(true,true,midp(X1,sk21,sk21),true),true),
inference(step,[status(thm)],[t26144,t5762]) ).
cnf(t26146,plain,
true = ifeq(midp(X1,sk20,sk22),true,midp(X1,sk21,sk21),true),
inference(step,[status(thm)],[t26145,t256]) ).
cnf(t22991,plain,
ifeq(midp(X1,sk20,sk22),true,midp(X1,sk21,sk21),true) = true,
inference(orient,[status(thm)],[t26146]) ).
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(t25,plain,
midp(sk23,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi113]) ).
cnf(t1831,plain,
midp(sk23,sk20,sk22) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(t22996,plain,
true = ifeq(true,true,midp(sk23,sk21,sk21),true),
inference(cp,[status(thm)],[t22991,t1831]) ).
cnf(t26147,plain,
true = midp(sk23,sk21,sk21),
inference(step,[status(thm)],[t22996,t256]) ).
cnf(t22997,plain,
midp(sk23,sk21,sk21) = true,
inference(orient,[status(thm)],[t26147]) ).
cnf(t23354,plain,
true = ifeq(true,true,midp(sk23,X1,X1),true),
inference(cp,[status(thm)],[t23345,t22997]) ).
cnf(t26182,plain,
true = midp(sk23,X1,X1),
inference(step,[status(thm)],[t23354,t256]) ).
cnf(t23355,plain,
midp(sk23,X1,X1) = true,
inference(orient,[status(thm)],[t26182]) ).
cnf(t23356,plain,
true = ifeq(true,true,cong(sk23,X1,sk23,X1),true),
inference(cp,[status(thm)],[t316,t23355]) ).
cnf(t26183,plain,
true = cong(sk23,X1,sk23,X1),
inference(step,[status(thm)],[t23356,t256]) ).
cnf(t23375,plain,
cong(sk23,X1,sk23,X1) = true,
inference(orient,[status(thm)],[t26183]) ).
cnf(t23392,plain,
true = ifeq(true,true,ifeq(cong(sk23,X1,sk23,X1),true,perp(sk23,sk23,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t23375]) ).
cnf(t26185,plain,
true = ifeq(cong(sk23,X1,sk23,X1),true,perp(sk23,sk23,X2,X1),true),
inference(step,[status(thm)],[t23392,t256]) ).
cnf(t26186,plain,
true = ifeq(true,true,perp(sk23,sk23,X2,X1),true),
inference(step,[status(thm)],[t26185,t23375]) ).
cnf(t26187,plain,
true = perp(sk23,sk23,X2,X1),
inference(step,[status(thm)],[t26186,t256]) ).
cnf(t23445,plain,
perp(sk23,sk23,X1,X2) = true,
inference(orient,[status(thm)],[t26187]) ).
cnf(t23446,plain,
true = ifeq(true,true,perp(X1,X2,sk23,sk23),true),
inference(cp,[status(thm)],[t327,t23445]) ).
cnf(t26189,plain,
true = perp(X1,X2,sk23,sk23),
inference(step,[status(thm)],[t23446,t256]) ).
cnf(t23498,plain,
perp(X1,X2,sk23,sk23) = true,
inference(orient,[status(thm)],[t26189]) ).
cnf(t23502,plain,
true = ifeq(true,true,ifeq(perp(sk23,sk23,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t322,t23498]) ).
cnf(t26191,plain,
true = ifeq(perp(sk23,sk23,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t23502,t256]) ).
cnf(t26192,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t26191,t23445]) ).
cnf(t26193,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t26192,t256]) ).
cnf(t23555,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t26193]) ).
cnf(t26205,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)],[t313,t23555]) ).
cnf(t26206,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)],[t26205,t256]) ).
cnf(t26207,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t26206,t23555]) ).
cnf(t26208,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t26207,t256]) ).
cnf(t23562,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t26208]) ).
cnf(t24145,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t23562]) ).
cnf(t24186,plain,
true = ifeq(true,true,midp(sk23,X1,X2),true),
inference(cp,[status(thm)],[t24145,t23355]) ).
cnf(t26276,plain,
true = midp(sk23,X1,X2),
inference(step,[status(thm)],[t24186,t256]) ).
cnf(t24207,plain,
midp(sk23,X1,X2) = true,
inference(orient,[status(thm)],[t26276]) ).
cnf(t26277,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t5927,t24207]) ).
cnf(t26278,plain,
false = true,
inference(step,[status(thm)],[t26277,t256]) ).
cnf(t24216,plain,
false = true,
inference(rw,[status(thm)],[t26278]) ).
cnf(t24217,plain,
false = true,
inference(orient,[status(thm)],[t24216]) ).
cnf(t26279,plain,
cong(sk23,sk26,sk23,sk27) = true,
inference(step,[status(thm)],[t3414,t24217]) ).
cnf(t24218,plain,
cong(sk23,sk26,sk23,sk27) = true,
inference(orient,[status(thm)],[t26279]) ).
cnf(goal_0,negated_conjecture,
cong(sk23,sk26,sk23,sk27) != true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t24218]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO623+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 12:34:49 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 168.62/22.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 168.62/22.28 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------