%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : PUZ047+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 : Tue Sep 29 12:30:50 PM UTC 2026
% Result : Theorem 0.18s 0.51s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ047+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 22:38:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.51 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.18/0.51
% 0.18/0.51 % SZS status Theorem
% 0.18/0.51
% 0.18/0.52 % SZS output start Proof
% 0.18/0.52 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.18/0.52 Axiom 2 (thm100): p(south, south, south, south, start) = true.
% 0.18/0.52 Axiom 3 (thm100_5): ifeq(p(south, south, north, south, X), true, p(north, south, north, north, take_cabbage(X)), true) = true.
% 0.18/0.52 Axiom 4 (thm100_1): ifeq(p(south, X, south, Y, Z), true, p(north, X, north, Y, take_goat(Z)), true) = true.
% 0.18/0.52 Axiom 5 (thm100_2): ifeq(p(south, south, south, north, X), true, p(north, north, south, north, take_wolf(X)), true) = true.
% 0.18/0.53 Axiom 6 (thm100_8): ifeq(p(north, X, north, Y, Z), true, p(south, X, south, Y, take_goat(Z)), true) = true.
% 0.18/0.53 Axiom 7 (thm100_9): ifeq(p(north, south, north, south, X), true, p(south, south, north, south, go_alone(X)), true) = true.
% 0.18/0.53 Axiom 8 (thm100_11): ifeq(p(north, north, south, north, X), true, p(south, north, south, north, go_alone(X)), true) = true.
% 0.18/0.53
% 0.18/0.53 Goal 1 (thm100_15): p(north, north, north, north, X) = true.
% 0.18/0.53 The goal is true when:
% 0.18/0.53 X = take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.18/0.53
% 0.18/0.53 Proof:
% 0.18/0.53 p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))))
% 0.18/0.53 = { by axiom 1 (ifeq_axiom) R->L }
% 0.18/0.53 ifeq(true, true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 8 (thm100_11) R->L }
% 0.18/0.53 ifeq(ifeq(p(north, north, south, north, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true, p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true), true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 1 (ifeq_axiom) R->L }
% 0.18/0.53 ifeq(ifeq(ifeq(true, true, p(north, north, south, north, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true), true, p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true), true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 6 (thm100_8) R->L }
% 0.18/0.53 ifeq(ifeq(ifeq(ifeq(p(north, south, north, north, take_cabbage(go_alone(take_goat(start)))), true, p(south, south, south, north, take_goat(take_cabbage(go_alone(take_goat(start))))), true), true, p(north, north, south, north, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true), true, p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true), true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 1 (ifeq_axiom) R->L }
% 0.18/0.53 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(north, south, north, north, take_cabbage(go_alone(take_goat(start)))), true), true, p(south, south, south, north, take_goat(take_cabbage(go_alone(take_goat(start))))), true), true, p(north, north, south, north, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true), true, p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true), true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 7 (thm100_9) R->L }
% 0.18/0.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(north, south, north, south, take_goat(start)), true, p(south, south, north, south, go_alone(take_goat(start))), true), true, p(north, south, north, north, take_cabbage(go_alone(take_goat(start)))), true), true, p(south, south, south, north, take_goat(take_cabbage(go_alone(take_goat(start))))), true), true, p(north, north, south, north, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true), true, p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true), true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 1 (ifeq_axiom) R->L }
% 0.18/0.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(north, south, north, south, take_goat(start)), true), true, p(south, south, north, south, go_alone(take_goat(start))), true), true, p(north, south, north, north, take_cabbage(go_alone(take_goat(start)))), true), true, p(south, south, south, north, take_goat(take_cabbage(go_alone(take_goat(start))))), true), true, p(north, north, south, north, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true), true, p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true), true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 2 (thm100) R->L }
% 0.18/0.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(south, south, south, south, start), true, p(north, south, north, south, take_goat(start)), true), true, p(south, south, north, south, go_alone(take_goat(start))), true), true, p(north, south, north, north, take_cabbage(go_alone(take_goat(start)))), true), true, p(south, south, south, north, take_goat(take_cabbage(go_alone(take_goat(start))))), true), true, p(north, north, south, north, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true), true, p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true), true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 4 (thm100_1) }
% 0.18/0.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(south, south, north, south, go_alone(take_goat(start))), true), true, p(north, south, north, north, take_cabbage(go_alone(take_goat(start)))), true), true, p(south, south, south, north, take_goat(take_cabbage(go_alone(take_goat(start))))), true), true, p(north, north, south, north, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true), true, p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true), true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 1 (ifeq_axiom) }
% 0.18/0.53 ifeq(ifeq(ifeq(ifeq(ifeq(p(south, south, north, south, go_alone(take_goat(start))), true, p(north, south, north, north, take_cabbage(go_alone(take_goat(start)))), true), true, p(south, south, south, north, take_goat(take_cabbage(go_alone(take_goat(start))))), true), true, p(north, north, south, north, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true), true, p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true), true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 3 (thm100_5) }
% 0.18/0.53 ifeq(ifeq(ifeq(ifeq(true, true, p(south, south, south, north, take_goat(take_cabbage(go_alone(take_goat(start))))), true), true, p(north, north, south, north, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true), true, p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true), true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 1 (ifeq_axiom) }
% 0.18/0.53 ifeq(ifeq(ifeq(p(south, south, south, north, take_goat(take_cabbage(go_alone(take_goat(start))))), true, p(north, north, south, north, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true), true, p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true), true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 5 (thm100_2) }
% 0.18/0.53 ifeq(ifeq(true, true, p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true), true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 1 (ifeq_axiom) }
% 0.18/0.53 ifeq(p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true, p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))), true)
% 0.18/0.53 = { by axiom 4 (thm100_1) }
% 0.18/0.53 true
% 0.18/0.53 % SZS output end Proof
% 0.18/0.53
% 0.18/0.53 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------