%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL088-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 : Sun Sep 27 06:57:40 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.49s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 16 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 33 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 37 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(trans_rtrancl,axiom,
! [VAR_0] : trans(rtrancl(VAR_0)),
file('theBenchmark.p',trans_rtrancl) ).
cnf(c_39,plain,
trans(rtrancl(A)),
inference(clausify,[status(thm)],[trans_rtrancl]) ).
fof(transD,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(pair(VAR_1,VAR_3),VAR_0)
| ~ member(pair(VAR_2,VAR_3),VAR_0)
| ~ member(pair(VAR_1,VAR_2),VAR_0)
| ~ trans(VAR_0) ),
file('theBenchmark.p',transD) ).
cnf(c_40,plain,
( member(pair(B,D),A)
| ~ member(pair(C,D),A)
| ~ member(pair(B,C),A)
| ~ trans(A) ),
inference(clausify,[status(thm)],[transD]) ).
cnf(c_41,plain,
( member(pair(A,D),rtrancl(C))
| ~ member(pair(B,D),rtrancl(C))
| ~ member(pair(A,B),rtrancl(C)) ),
inference(resolve,[status(thm)],[c_39,c_40]) ).
fof(ap_reduce1_2c1,axiom,
~ member(pair(comb_app(p,r),comb_app(z,r)),rtrancl(contract)),
file('theBenchmark.p',ap_reduce1_2c1) ).
cnf(c_42,plain,
~ member(pair(comb_app(p,r),comb_app(z,r)),rtrancl(contract)),
inference(clausify,[status(thm)],[ap_reduce1_2c1]) ).
fof(ap_reduce1_2h5,axiom,
member(pair(comb_app(p,r),comb_app(y,r)),rtrancl(contract)),
file('theBenchmark.p',ap_reduce1_2h5) ).
cnf(c_43,plain,
member(pair(comb_app(p,r),comb_app(y,r)),rtrancl(contract)),
inference(clausify,[status(thm)],[ap_reduce1_2h5]) ).
fof(ap_reduce1_2h4,axiom,
member(pair(y,z),contract),
file('theBenchmark.p',ap_reduce1_2h4) ).
cnf(c_44,plain,
member(pair(y,z),contract),
inference(clausify,[status(thm)],[ap_reduce1_2h4]) ).
fof(ap_reduce1_2h1,axiom,
member(r,comb),
file('theBenchmark.p',ap_reduce1_2h1) ).
cnf(c_47,plain,
member(r,comb),
inference(clausify,[status(thm)],[ap_reduce1_2h1]) ).
fof(reduction_rls_3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(pair(comb_app(VAR_0,VAR_2),VAR_3),rtrancl(contract))
| ~ member(pair(comb_app(VAR_1,VAR_2),VAR_3),rtrancl(contract))
| ~ member(VAR_2,comb)
| ~ member(pair(VAR_0,VAR_1),contract) ),
file('theBenchmark.p',reduction_rls_3) ).
cnf(c_49,plain,
( member(pair(comb_app(A,C),D),rtrancl(contract))
| ~ member(pair(comb_app(B,C),D),rtrancl(contract))
| ~ member(C,comb)
| ~ member(pair(A,B),contract) ),
inference(clausify,[status(thm)],[reduction_rls_3]) ).
fof(contract_combD2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_1,comb)
| ~ member(pair(VAR_0,VAR_1),contract) ),
file('theBenchmark.p',contract_combD2) ).
cnf(c_52,plain,
( member(B,comb)
| ~ member(pair(A,B),contract) ),
inference(clausify,[status(thm)],[contract_combD2]) ).
fof(reduction_refl,axiom,
! [VAR_0] :
( member(pair(VAR_0,VAR_0),rtrancl(contract))
| ~ member(VAR_0,comb) ),
file('theBenchmark.p',reduction_refl) ).
cnf(c_57,plain,
( member(pair(A,A),rtrancl(contract))
| ~ member(A,comb) ),
inference(clausify,[status(thm)],[reduction_refl]) ).
fof(comb_intros3,axiom,
! [VAR_0,VAR_1] :
( member(comb_app(VAR_0,VAR_1),comb)
| ~ member(VAR_1,comb)
| ~ member(VAR_0,comb) ),
file('theBenchmark.p',comb_intros3) ).
cnf(c_58,plain,
( member(comb_app(A,B),comb)
| ~ member(B,comb)
| ~ member(A,comb) ),
inference(clausify,[status(thm)],[comb_intros3]) ).
cnf(c_728,plain,
( member(pair(comb_app(p,r),A),rtrancl(contract))
| ~ member(pair(comb_app(y,r),A),rtrancl(contract)) ),
inference(resolve,[status(thm)],[c_41,c_43]) ).
cnf(c_176,plain,
~ member(pair(comb_app(y,r),comb_app(z,r)),rtrancl(contract)),
inference(resolve,[status(thm)],[c_728,c_42]) ).
cnf(c_206,plain,
member(z,comb),
inference(resolve,[status(thm)],[c_52,c_44]) ).
cnf(c_729,plain,
( member(pair(comb_app(y,A),B),rtrancl(contract))
| ~ member(pair(comb_app(z,A),B),rtrancl(contract))
| ~ member(A,comb) ),
inference(resolve,[status(thm)],[c_49,c_44]) ).
cnf(c_730,plain,
( member(pair(comb_app(y,r),A),rtrancl(contract))
| ~ member(pair(comb_app(z,r),A),rtrancl(contract)) ),
inference(resolve,[status(thm)],[c_729,c_47]) ).
cnf(c_332,plain,
~ member(pair(comb_app(z,r),comb_app(z,r)),rtrancl(contract)),
inference(resolve,[status(thm)],[c_730,c_176]) ).
cnf(c_721,plain,
~ member(comb_app(z,r),comb),
inference(resolve,[status(thm)],[c_57,c_332]) ).
cnf(c_731,plain,
( member(comb_app(A,r),comb)
| ~ member(A,comb) ),
inference(resolve,[status(thm)],[c_58,c_47]) ).
cnf(c_732,plain,
~ member(z,comb),
inference(resolve,[status(thm)],[c_731,c_721]) ).
cnf(c_727,plain,
$false,
inference(resolve,[status(thm)],[c_206,c_732]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL088-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 23:16:00 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 1033536 was started by sandbox on n015,
% 0.11/0.38 % Sat Sep 26 23:16:00 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.49
% 0.14/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.49
% 0.14/0.49 % Proof 1 at 0.10 (+ 0.01) seconds.
% 0.14/0.49 % Length of proof is 16.
% 0.14/0.49 % Level of proof is 5.
% 0.14/0.49 % Maximum clause weight is 39.000.
% 0.14/0.49 % Given clauses 112.
% 0.14/0.49
% 0.14/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------