%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO077-4 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:19:14 PM UTC 2026
% Result : Unsatisfiable 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of clauses : 54 ( 32 unt; 20 nHn; 54 RR)
% Number of literals : 164 ( 49 equ; 82 neg)
% Maximal clause size : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 51 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_G1B,axiom,
( on(X1,line_from_to(X2,X1))
| X2 = X1
| ~ point(X2)
| ~ point(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G1B) ).
cnf(point2,hypothesis,
point(point2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2) ).
cnf(axiom_G1C,axiom,
( line(line_from_to(X1,X2))
| X1 = X2
| ~ point(X1)
| ~ point(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G1C) ).
cnf(point1,hypothesis,
point(point1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1) ).
cnf(point1_not_point2,hypothesis,
point1 != point2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_not_point2) ).
cnf(axiom_G1A,axiom,
( on(X1,line_from_to(X1,X2))
| X1 = X2
| ~ point(X1)
| ~ point(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G1A) ).
cnf(axiom_G1D,axiom,
( X1 = X3
| X2 = X4
| ~ on(X1,X2)
| ~ on(X3,X2)
| ~ on(X1,X4)
| ~ on(X3,X4)
| ~ point(X1)
| ~ point(X3)
| ~ line(X2)
| ~ line(X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G1D) ).
cnf(point1_on_line,hypothesis,
on(point1,a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_on_line) ).
cnf(line,hypothesis,
line(a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',line) ).
cnf(point2_on_line,hypothesis,
on(point2,a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2_on_line) ).
cnf(axiom_G10D,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| line(line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10D) ).
cnf(prove_points_noncollinear,negated_conjecture,
collinear(point1,point2,point3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_points_noncollinear) ).
cnf(point3,hypothesis,
point(point3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point3) ).
cnf(point2_not_point3,hypothesis,
point2 != point3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2_not_point3) ).
cnf(point1_not_point3,hypothesis,
point1 != point3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_not_point3) ).
cnf(axiom_G10A,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| on(X1,line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10A) ).
cnf(axiom_G10B,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| on(X2,line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10B) ).
cnf(axiom_G10C,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| on(X3,line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10C) ).
cnf(point3_not_on_line,hypothesis,
~ on(point3,a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point3_not_on_line) ).
cnf(c_0_19,axiom,
( on(X1,line_from_to(X2,X1))
| X2 = X1
| ~ point(X2)
| ~ point(X1) ),
axiom_G1B ).
cnf(c_0_20,hypothesis,
point(point2),
point2 ).
cnf(c_0_21,axiom,
( line(line_from_to(X1,X2))
| X1 = X2
| ~ point(X1)
| ~ point(X2) ),
axiom_G1C ).
cnf(c_0_22,hypothesis,
point(point1),
point1 ).
cnf(c_0_23,hypothesis,
( X1 = point2
| on(X1,line_from_to(point2,X1))
| ~ point(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,hypothesis,
point1 != point2,
point1_not_point2 ).
cnf(c_0_25,hypothesis,
( X1 = point1
| line(line_from_to(X1,point1))
| ~ point(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
( on(X1,line_from_to(X1,X2))
| X1 = X2
| ~ point(X1)
| ~ point(X2) ),
axiom_G1A ).
cnf(c_0_27,axiom,
( X1 = X3
| X2 = X4
| ~ on(X1,X2)
| ~ on(X3,X2)
| ~ on(X1,X4)
| ~ on(X3,X4)
| ~ point(X1)
| ~ point(X3)
| ~ line(X2)
| ~ line(X4) ),
axiom_G1D ).
cnf(c_0_28,hypothesis,
on(point1,line_from_to(point2,point1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_24]) ).
cnf(c_0_29,hypothesis,
line(line_from_to(point2,point1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_24]) ).
cnf(c_0_30,hypothesis,
( X1 = point1
| on(X1,line_from_to(X1,point1))
| ~ point(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_31,hypothesis,
( X1 = line_from_to(point2,point1)
| X2 = point1
| ~ line(X1)
| ~ point(X2)
| ~ on(X2,line_from_to(point2,point1))
| ~ on(point1,X1)
| ~ on(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_22])]) ).
cnf(c_0_32,hypothesis,
on(point2,line_from_to(point2,point1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_20]),c_0_24]) ).
cnf(c_0_33,hypothesis,
( X1 = line_from_to(point2,point1)
| ~ line(X1)
| ~ on(point1,X1)
| ~ on(point2,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_20])]),c_0_24]) ).
cnf(c_0_34,hypothesis,
on(point1,a_line),
point1_on_line ).
cnf(c_0_35,hypothesis,
line(a_line),
line ).
cnf(c_0_36,hypothesis,
on(point2,a_line),
point2_on_line ).
cnf(c_0_37,hypothesis,
line_from_to(point2,point1) = a_line,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36])]) ).
cnf(c_0_38,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| line(line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
axiom_G10D ).
cnf(c_0_39,negated_conjecture,
collinear(point1,point2,point3),
prove_points_noncollinear ).
cnf(c_0_40,hypothesis,
point(point3),
point3 ).
cnf(c_0_41,hypothesis,
point2 != point3,
point2_not_point3 ).
cnf(c_0_42,hypothesis,
point1 != point3,
point1_not_point3 ).
cnf(c_0_43,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| on(X1,line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
axiom_G10A ).
cnf(c_0_44,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| on(X2,line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
axiom_G10B ).
cnf(c_0_45,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| on(X3,line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
axiom_G10C ).
cnf(c_0_46,hypothesis,
( X1 = a_line
| ~ line(X1)
| ~ on(point1,X1)
| ~ on(point2,X1) ),
inference(rw,[status(thm)],[c_0_33,c_0_37]) ).
cnf(c_0_47,negated_conjecture,
line(line_through_3_points(point1,point2,point3)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_20]),c_0_22])]),c_0_41]),c_0_42]),c_0_24]) ).
cnf(c_0_48,negated_conjecture,
on(point1,line_through_3_points(point1,point2,point3)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_40]),c_0_20]),c_0_22])]),c_0_41]),c_0_42]),c_0_24]) ).
cnf(c_0_49,negated_conjecture,
on(point2,line_through_3_points(point1,point2,point3)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_39]),c_0_40]),c_0_20]),c_0_22])]),c_0_41]),c_0_42]),c_0_24]) ).
cnf(c_0_50,negated_conjecture,
on(point3,line_through_3_points(point1,point2,point3)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_39]),c_0_40]),c_0_20]),c_0_22])]),c_0_41]),c_0_42]),c_0_24]) ).
cnf(c_0_51,negated_conjecture,
line_through_3_points(point1,point2,point3) = a_line,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_52,hypothesis,
~ on(point3,a_line),
point3_not_on_line ).
cnf(c_0_53,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO077-4 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n011.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:39:47 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.369s
%------------------------------------------------------------------------------